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## Murat, François

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 Author ID: murat.francois Published as: Murat, F.; Murat, Francois; Murat, François Homepage: https://www.ljll.math.upmc.fr/membres/fiches/murat.html External Links: MGP · dblp
 Documents Indexed: 161 Publications since 1971, including 4 Books
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#### Co-Authors

 13 single-authored 24 Boccardo, Lucio 12 Casado-Díaz, Juan 9 Giachetti, Daniela 9 Puel, Jean-Pierre 8 Charalambakis, Nicolas Ch. 8 Francfort, Gilles A. 8 Sili, Ali 7 Dal Maso, Gianni 7 Tartar, Luc C. 6 Bernardi, Christine 6 Lewandowski, Roger 6 Mercaldo, Anna 6 Mokrane, Abdelhafid 5 Betta, Maria Francesca 5 Girault, Vivette 5 Martínez-Aparicio, Pedro J. 5 Mignot, Fulbert 5 Porretta, Alessio 5 Porzio, Maria Michaela 4 Bensoussan, Alain 4 Chacón Rebollo, Tomás 4 Cioranescu, Doina 4 Conca, Carlos 4 Luna-Laynez, Manuel 4 Pironneau, Olivier 4 Rebollo, T. Chacón 3 Ball, John M. 3 Blanchard, Dominique 3 Briane, Marc 3 Chatzigeorgiou, George 3 Ferone, Vincenzo 3 Gallouët, Thierry 3 Gaudiello, Antonio 3 Gómez Mármol, Macarena 3 Haraux, Alain 3 Joseph, Anthony 3 Paroni, Roberto 3 Prum, Bernard 3 Rentschler, Rudolf 2 Bègue, Catherine 2 Brahim-Otsmane, Safia 2 Diaz Diaz, Jesus Ildefonso 2 Farroni, Fernando 2 Freddi, Lorenzo 2 Grenon, Nathalie 2 Lions, Jacques-Louis 2 Mokobodzki, Gabriel 2 Monneau, Régis 2 Mossino, Jacqueline 2 Orsina, Luigi 2 Prignet, Alain 2 Redwane, Hicham 2 Sbordone, Carlo 1 Allaire, Grégoire 1 Alvino, Angelo 1 Amirat, Youcef Aït 1 Azaïez, Mejdi 1 Barles, Guy 1 Ben Belgacem, Faker 1 Blouza, Adel 1 Chacon, Tomas 1 Dacorogna, Bernard 1 Dall’Aglio, Andrea 1 Danaila, Ionut 1 Dib, Séréna 1 Donato, Patrizia 1 Finzi Vita, Stefano 1 Giova, Raffaella 1 Guibé, Olivier 1 Hamdache, Kamel 1 Hamour, Boussad 1 Hecht, Frédéric 1 Joly, Pascal 1 Kaber, Sidimahmoud 1 Kacimi, Hayat 1 Lederer, Johannes 1 LeFloch, Philippe Gerard 1 Lucquin, Brigitte 1 Moscariello, Gioconda 1 Peral Alonso, Ireneo 1 Postel, Marie 1 Salgado, Abner J. 1 Sayah, Toni 1 Simon, Jacques 1 Tatar, Luc 1 Tchou, Nicoletta Anna 1 Timofte, Claudia 1 Trombetti, Cristina 1 Zuazua, Enrique
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#### Serials

 7 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 7 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 7 Comptes Rendus de l’Académie des Sciences. Série I 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 4 Archive for Rational Mechanics and Analysis 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Journal of Differential Equations 4 Journal of Functional Analysis 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 SIAM Journal on Mathematical Analysis 3 Numerische Mathematik 3 Ricerche di Matematica 3 Asymptotic Analysis 3 Communications in Partial Differential Equations 3 Progress in Mathematics 3 Nonlinear Analysis. Theory, Methods & Applications 2 International Journal of Solids and Structures 2 Portugaliae Mathematica 2 Quarterly of Applied Mathematics 2 SIAM Journal on Numerical Analysis 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Potential Analysis 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Bollettino della Unione Matematica Italiana. Serie VIII. Sezione B. Articoli di Ricerca Matematica 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 2 Bollettino dell’Unione Matematica Italiana. Series IX 2 Bollettino dell’Unione Matematica Italiana 1 Communications on Pure and Applied Mathematics 1 International Journal of Engineering Science 1 Applied Mathematics and Optimization 1 Gazette des Mathématiciens 1 Japanese Journal of Mathematics. New Series 1 Le Matematiche 1 Proceedings of the American Mathematical Society 1 Zeitschrift für Analysis und ihre Anwendungen 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Atti del Seminario Matematico e Fisico dell’Università di Modena 1 Notices of the American Mathematical Society 1 Calculus of Variations and Partial Differential Equations 1 Séminaire Équations aux Dérivées Partielles 1 Discrete and Continuous Dynamical Systems 1 Mathematics and Mechanics of Solids 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Journal of Mathematical Fluid Mechanics 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Bulletin de la Société Mathématique de France. Supplément. Mémoires 1 Quaderni di Matematica 1 Networks and Heterogeneous Media
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#### Fields

 128 Partial differential equations (35-XX) 28 Calculus of variations and optimal control; optimization (49-XX) 25 Mechanics of deformable solids (74-XX) 14 Operator theory (47-XX) 13 Functional analysis (46-XX) 13 Fluid mechanics (76-XX) 10 Numerical analysis (65-XX) 5 General and overarching topics; collections (00-XX) 4 Potential theory (31-XX) 3 Real functions (26-XX) 2 History and biography (01-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Geophysics (86-XX) 2 Systems theory; control (93-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Integral equations (45-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

135 Publications have been cited 4,108 times in 2,647 Documents Cited by Year
Definition and weak stability of nonconservative products. Zbl 0853.35068
Dal Maso, Gianni; LeFloch, Philippe G.; Murat, François
1995
Compacite par compensation. Zbl 0399.46022
Murat, Francois
1978
Renormalization solutions of elliptic equations with general measure data. Zbl 0958.35045
Dal Maso, Gianni; Murat, François; Orsina, Luigi; Prignet, Alain
1999
$$W^{1,p}$$-quasiconvexity and variational problems for multiple integrals. Zbl 0549.46019
Ball, J. M.; Murat, F.
1984
Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations. Zbl 0783.35020
Boccardo, Lucio; Murat, François
1992
Existence of bounded solutions for non linear elliptic unilateral problems. Zbl 0687.35042
Boccardo, L.; Murat, F.; Puel, J. P.
1988
Renormalised solutions of nonlinear parabolic problems with $$L^1$$ data: Existence and uniqueness. Zbl 0895.35050
Blanchard, D.; Murat, F.
1997
$$H$$-convergence. Zbl 0920.35019
Murat, François; Tartar, Luc
1997
Un terme etrange venu d’ailleurs. Zbl 0496.35030
Cioranescu, D.; Murat, F.
1982
L’injection du cône positif de $$H^{-1}$$ dans $$W^{1,q}$$ est compacte pour tout $$q<2$$ (avec remarque par Haim Brezis). Zbl 0471.46020
Murat, Francois
1981
Homogenization and optimal bounds in linear elasticity. Zbl 0604.73013
Francfort, G. A.; Murat, F.
1986
$$L^{\infty{}}$$ estimate for some nonlinear elliptic partial differential equations and application to an existence result. Zbl 0785.35033
Boccardo, L.; Murat, F.; Puel, J.-P.
1992
Compacite par compensation: condition necessaire et suffisante de continuite faible sous une hypothèse de rang constant. Zbl 0464.46034
Murat, Francois
1981
Existence and uniqueness of a renormalized solution for a fairly general class of nonlinear parabolic problems. Zbl 0998.35030
Blanchard, Dominique; Murat, François; Redwane, Hicham
2001
On a nonlinear partial differential equation having natural growth terms and unbounded solution. Zbl 0696.35042
Bensoussan, A.; Boccardo, L.; Murat, F.
1988
Existence and regularity of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms. Zbl 0803.35046
Boccardo, L.; Giachetti, D.; Diaz, J. I.; Murat, F.
1993
Existence de solutions non bornées pour certaines équations quasi- linéaires. Zbl 0524.35041
Boccardo, L.; Murat, F.; Puel, J. P.
1982
Résultats d’existence pour certains problèmes elliptiques quasilinéaires. (Existence results for certain quasilinear elliptic problems). Zbl 0557.35051
Boccardo, L.; Murat, F.; Puel, J. P.
1984
The Stokes and Navier-Stokes equations with boundary conditions involving the pressure. Zbl 0826.35093
Conca, C.; Murat, F.; Pironneau, O.
1994
Correctors for the homogenization of the wave and heat equations. Zbl 0837.35016
Brahim-Otsmane, S.; Francfort, G. A.; Murat, F.
1992
A strange term coming from nowhere. Zbl 0912.35020
Cioranescu, Doina; Murat, François
1997
Existence de solutions faibles pour des équations elliptiques quasi- linéaires à croissance quadratique. (Existence of weak solutions for quasilinear elliptic equations with quadratic growth). Zbl 0588.35041
Boccardo, L.; Murat, F.; Puel, J.-P.
1983
Nonlinear problems having natural growth in the gradient: an existence result when the source terms are small. Zbl 1158.35358
Ferone, Vincenzo; Murat, François
2000
Existence results for some quasilinear parabolic equations. Zbl 0705.35066
Boccardo, Lucio; Murat, François; Puel, Jean-Pierre
1989
Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions. Zbl 0859.35031
Barles, Guy; Murat, François
1995
Remarks on Chacon’s biting lemma. Zbl 0678.46023
Ball, J. M.; Murat, F.
1989
Almost everywhere convergence of gradients of solutions to nonlinear elliptic systems. Zbl 0890.35039
Dal Maso, Gianni; Murat, François
1998
Contre-exemples pour divers problèmes ou le contrôle intervient dans les coefficients. Zbl 0349.49005
Murat, Francois
1977
Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators. Zbl 0899.35007
Dal Maso, Gianni; Murat, François
1997
Étude de problèmes d’optimal design. Zbl 0334.49013
Murat, Francois; Simon, Jacques
1976
Existence of renormalized solutions to nonlinear elliptic equations with lower-order terms and right-hand side a measure. Zbl 1165.35365
Betta, Maria Francesca; Mercaldo, Anna; Murat, François; Porzio, Maria Michaela
2003
Homogenization of the Neumann problem with nonisolated holes. Zbl 0823.35014
Allaire, Grégoire; Murat, François
1993
An elliptic problem with a lower order term having singular behaviour. Zbl 1173.35469
Giachetti, Daniela; Murat, François
2009
Les équations de Stokes et de Navier-Stokes avec des conditions aux limites sur la pression. (On Stokes and Navier-Stokes equations with boundary condition on the pressure). Zbl 0687.35069
Begue, C.; Conca, C.; Murat, F.; Pironneau, O.
1988
Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains. Zbl 1110.35008
Dal Maso, Gianni; Murat, François
2004
Quasilinear problems having quadratic growth in the gradient: An existence result when the source term is small. Zbl 0917.35039
Ferone, Vincenzo; Murat, François
1998
Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in $$L^1(\Omega)$$. Zbl 1092.35032
Betta, M. F.; Mercaldo, A.; Murat, F.; Porzio, M. M.
2002
Optimality conditions and homogenization. Zbl 0569.49015
Murat, F.; Tartar, L.
1985
Un contre-exemple pour le problème du contrôle dans les coefficients. (A counter-example for the control problem in the coefficients.). Zbl 0235.49011
Murat, François
1971
Oscillations and energy densities in the wave equation. Zbl 0803.35010
Francfort, G. A.; Murat, F.
1992
Unicité de la solution de certaines équations elliptiques non linéaires. (Uniqueness of the solution of some nonlinear elliptic equations). Zbl 0789.35056
Boccardo, Lucio; Gallouët, Thierry; Murat, François
1992
Remarques sur l’homogénéisation de certains problèmes quasi- linéaires. Zbl 0524.35042
Boccardo, Lucio; Murat, François
1982
Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms. Zbl 1149.35352
Grenon, Nathalie; Murat, François; Porretta, Alessio
2005
Asymptotic behavior of solutions of the anisotropic heterogeneous linearized elasticity system in thin cylinders. Zbl 0929.74010
Murat, François; Sili, Ali
1999
Definition and existence of renormalized solutions of elliptic equations with general measure data. Zbl 0887.35057
Dal Maso, Gianni; Murat, François; Orsina, Luigi; Prignet, Alain
1997
A semilinear elliptic equation with a mild singularity at $$u=0$$: existence and homogenization. Zbl 1371.35112
Giachetti, Daniela; Martínez-Aparicio, Pedro J.; Murat, François
2017
Uniqueness results for nonlinear elliptic equations with a lower order term. Zbl 1125.35343
Betta, M. Francesca; Mercaldo, Anna; Murat, François; Porzio, M. Michaela
2005
Variation d’un point de retournement par rapport au domaine. Zbl 0422.35039
Mignot, F.; Murat, F.; Puel, J. P.
1979
A priori estimates and existence for elliptic equations with gradient dependent terms. Zbl 1305.35058
Grenon, Nathalie; Murat, François; Porretta, Alessio
2014
Global weak solutions to equations of motion for magnetic fluids. Zbl 1162.76408
Amirat, Youcef; Hamdache, Kamel; Murat, François
2008
Calculus of variations and homogenization. Zbl 0939.35019
Murat, François; Tartar, Luc
1997
Stability properties, existence, and nonexistence of renormalized solutions for elliptic equations with measure data. Zbl 1129.35397
Murat, F.; Porretta, A.
2002
Quelques propriétés des opérateurs elliptiques quasi linéaires. (Some properties of quasilinear elliptic operators). Zbl 0696.35050
Boccardo, Lucio; Murat, François; Puel, Jean-Pierre
1988
On the junction of elastic plates and beams. Zbl 1032.74037
Gaudiello, Antonio; Monneau, Régis; Mossino, Jacqueline; Murat, François; Sili, Ali
2002
A nouveau sur les équations de Stokes et de Navier-Stokes avec des conditions aux limites sur la pression. (Going back to Stokes and Navier- Stokes equations with boundary conditions on the pressure). Zbl 0613.76029
Bègue, Catherine; Conca, Carlos; Murat, François; Pironneau, Olivier
1987
The div-curl lemma “trente ans après”: an extension and an application to the $$G$$-convergence of unbounded monotone operators. Zbl 1183.35012
Briane, M.; Casado-Díaz, J.; Murat, F.
2009
Junction of elastic plates and beams. Zbl 1133.35322
Gaudiello, Antonio; Monneau, Régis; Mossino, Jacqueline; Murat, François; Sili, Ali
2007
On a turbulent system with unbounded eddy viscosities. Zbl 1013.35068
Gallouët, T.; Lederer, J.; Lewandowski, R.; Murat, F.; Tartar, L.
2003
A unified presentation of two existence results for problems with natural growth. Zbl 0806.35033
Boccardo, L.; Gallouët, T.; Murat, F.
1993
Existence of a solution for a weaker form of a nonlinear elliptic equation. Zbl 0703.35063
Boccardo, L.; Diaz, J. I.; Giachetti, D.; Murat, F.
1989
Existence and uniqueness of a renormalized solution for a fairly general nonlinear parabolic problem. Zbl 0935.35073
Blanchard, Dominique; Murat, François; Redwane, Hicham
1999
$$H$$ convergence for quasi-linear elliptic equations with quadratic growth. Zbl 0795.35008
Bensoussan, A.; Boccardo, L.; Murat, F.
1992
Un terme etrange venu d’ailleurs. II. Zbl 0498.35034
Cioranescu, Doina; Murat, Francois
1982
Existence and uniqueness results for nonlinear elliptic problems with a lower order term and measure datum. Zbl 1016.35026
Betta, M. Francesca; Mercaldo, Anna; Murat, François; Porzio, M. Michaela
2002
The Neumann sieve. Zbl 0586.35037
Murat, F.
1985
Nonlinear elliptic equations with natural growth in the gradient and source terms in Lorentz spaces. Zbl 1318.35031
Ferone, Vincenzo; Murat, François
2014
Homogenization of elliptic equations with principal part not in divergence form and Hamiltonian with quadratic growth. Zbl 0602.35030
Bensoussan, A.; Boccardo, L.; Murat, F.
1986
Théorèmes de non-existence pour des problèmes de contrôle dans les coefficients. (Non-existence theorems for the control system in the coefficients.). Zbl 0235.49012
Murat, François
1972
Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in $$L^1$$. Zbl 1144.65072
Casado-Díaz, J.; Chacón Rebollo, T.; Girault, V.; Gómez Mármol, M.; Murat, F.
2007
Monotone operators in divergence form with $$X$$-dependent multivalued graphs. Zbl 1115.35047
Francfort, Gilles; Murat, François; Tatar, Luc
2004
A model for two coupled turbulent fluids. I: Analysis of the system. Zbl 1034.35106
Bernardi, C.; Chacón Rebollo, T.; Lewandowski, R.; Murat, F.
2002
On the optimality of certain Sobolev exponents for the weak continuity of determinants. Zbl 0769.46025
Dacorogna, B.; Murat, F.
1992
Nouveaux résultats de convergence dans des problèmes unilateraux. Zbl 0484.49009
Boccardo, L.; Murat, F.
1982
Compacite par compensation II. Zbl 0427.35008
Murat, F.
1979
A model for two coupled turbulent fluids. II: Numerical analysis of a spectral discretization. Zbl 1129.76327
Bernardi, C.; Chacón Rebollo, T.; Lewandowski, R.; Murat, F.
2003
Definition, existence, stability and uniqueness of the solution to a semilinear elliptic problem with a strong singularity at $$u = 0$$. Zbl 1407.35076
Giachetti, Daniela; Martínez-Aparicio, Pedro J.; Murat, François
2018
Homogenization of the brush problem with a source term in $$L^{1}$$. Zbl 1371.35067
Gaudiello, Antonio; Guibé, Olivier; Murat, François
2017
Homogenization of monotone operators in divergence form with $$x$$-dependent multivalued graphs. Zbl 1180.35077
Francfort, Gilles A.; Murat, François; Tartar, Luc
2009
Uniqueness results for pseudomonotone problems with $$p>2$$. Zbl 1118.35307
Casado-Díaz, Juan; Murat, François; Porretta, Alessio
2007
The Lewy-Stampacchia inequality for bilateral problems. Zbl 1121.35066
Mokrane, Abdelhafid; Murat, François
2004
A model for two coupled turbulent fluids. III: Numerical approximation by finite elements. Zbl 1129.76326
Bernardi, C.; Chacón Rebollo, T.; Gómez Mármol, M.; Lewandowski, R.; Murat, F.
2004
Nonlocal effects in the passage from 3d to 1d in linearized, anisotropic, heterogeneous elasticity. Zbl 0962.74009
Murat, François; Sili, Ali
2000
Fourth-order moments of nonnegative measures on $$S^ 2$$ and applications. Zbl 0869.73006
Francfort, Gilles; Murat, François; Tartar, Luc
1995
Homogenization of nonlinear unilateral problems. Zbl 0749.49009
Boccardo, Lucio; Murat, François
1991
Anisotropic inhomogeneous rectangular thin-walled beams. Zbl 1170.49014
Freddi, Lorenzo; Murat, François; Paroni, Roberto
2009
Homogenization problems of a hollow cylinder made of elastic materials with discontinuous properties. Zbl 1169.74532
Chatzigeorgiou, George; Charalambakis, Nicolas; Murat, Francois
2008
Homogenization of stratified thermoviscoplastic materials. Zbl 1144.74364
Charalambakis, Nicolas; Murat, François
2006
The Lewy–Stampacchia inequality for the obstacle problem with quadratic growth in the gradient. Zbl 1105.35041
Murat, F.; Mokrane, A.
2005
Monotonous problems in cylinders consisting of heterogeneous material with vanishing diameter. Zbl 0833.35140
Murat, François; Sili, Ali
1995
Remarks on rank-one convexity and quasi convexity. Zbl 0751.49005
Ball, J. M.; Murat, F.
1991
Weak solutions to the initial-boundary value problem for the shearing of non-homogeneous thermoviscoplastic materials. Zbl 0686.73007
Charalambakis, Nicolas; Murat, François
1989
The diffusion equation in a notched beam. Zbl 1136.35323
Casado-Díaz, Juan; Luna-Laynez, Manuel; Murat, François
2008
Asymptotic behavior of diffusion problems in a domain made of two cylinders of different diameters and lengths. Zbl 1188.35058
Casado-Díaz, Juan; Luna-Laynez, Manuel; Murat, François
2004
On the control of coefficients in partial differential equations. Zbl 0913.35020
Murat, François; Tartar, Luc
1997
Homogenization and corrector for the wave equation in domains with small holes. Zbl 0807.35077
Cioranescu, D.; Donato, P.; Murat, F.; Zuazua, E.
1991
Homogenization of a Dirichlet semilinear elliptic problem with a strong singularity at $$u=0$$ in a domain with many small holes. Zbl 1387.35030
Giachetti, Daniela; Martínez-Aparicio, Pedro J.; Murat, François
2018
Analysis of a coupled fluid-structure model with applications to hemodynamics. Zbl 1343.35184
Chacón Rebollo, T.; Girault, V.; Murat, F.; Pironneau, O.
2016
Asymptotic behavior of an elastic beam fixed on a small part of one of its extremities. Zbl 1058.74047
Casado-Díaz, Juan; Luna-Laynez, Manuel; Murat, François
2004
A generalized strange term in Signorini’s type problems. Zbl 1040.35008
Conca, Carlos; Murat, François; Timofte, Claudia
2003
A proof of the Lewy-Stampacchia’s inequality by a penalization method. Zbl 0918.35058
Mokrane, A.; Murat, F.
1998
Definition, existence, stability and uniqueness of the solution to a semilinear elliptic problem with a strong singularity at $$u = 0$$. Zbl 1407.35076
Giachetti, Daniela; Martínez-Aparicio, Pedro J.; Murat, François
2018
Homogenization of a Dirichlet semilinear elliptic problem with a strong singularity at $$u=0$$ in a domain with many small holes. Zbl 1387.35030
Giachetti, Daniela; Martínez-Aparicio, Pedro J.; Murat, François
2018
On the definition of the solution to a semilinear elliptic problem with a strong singularity at $$u = 0$$. Zbl 1408.35026
Giachetti, Daniela; Martínez-Aparicio, Pedro J.; Murat, François
2018
Finite element methods for Darcy’s problem coupled with the heat equation. Zbl 1393.35159
Bernardi, Christine; Dib, Séréna; Girault, Vivette; Hecht, Frédéric; Murat, François; Sayah, Toni
2018
A new algorithm of proper generalized decomposition for parametric symmetric elliptic problems. Zbl 1447.35145
Azaïez, M.; Ben Belgacem, F.; Casado-Díaz, J.; Rebollo, T. Chacón; Murat, F.
2018
A semilinear elliptic equation with a mild singularity at $$u=0$$: existence and homogenization. Zbl 1371.35112
Giachetti, Daniela; Martínez-Aparicio, Pedro J.; Murat, François
2017
Homogenization of the brush problem with a source term in $$L^{1}$$. Zbl 1371.35067
Gaudiello, Antonio; Guibé, Olivier; Murat, François
2017
Increase of powers in the lower order term: a come back when the source term has a poor summability. Zbl 1391.35135
Boccardo, L.; Murat, F.
2017
Analysis of a coupled fluid-structure model with applications to hemodynamics. Zbl 1343.35184
Chacón Rebollo, T.; Girault, V.; Murat, F.; Pironneau, O.
2016
Advances in the study of singular semilinear elliptic problems. Zbl 1403.35109
Giachetti, Daniela; Martínez-Aparicio, Pedro J.; Murat, François
2016
Quasilinear problems involving a perturbation with quadratic growth in the gradient and a noncoercive zeroth order term. Zbl 1341.35067
Hamour, Boussad; Murat, François
2016
A priori estimates and existence for elliptic equations with gradient dependent terms. Zbl 1305.35058
Grenon, Nathalie; Murat, François; Porretta, Alessio
2014
Nonlinear elliptic equations with natural growth in the gradient and source terms in Lorentz spaces. Zbl 1318.35031
Ferone, Vincenzo; Murat, François
2014
The behavior of a beam fixed on small sets of one of its extremities. Zbl 1299.74102
Casado-Díaz, Juan; Luna-Laynez, Manuel; Murat, Francois
2014
Lewy-Stampacchia’s inequality for a Leray-Lions operator with natural growth in the gradient. Zbl 1301.49025
Mokrane, A.; Murat, F.
2014
Finite element discretization of Darcy’s equations with pressure-dependent porosity. Zbl 1271.76166
Girault, Vivette; Murat, François; Salgado, Abner
2010
Saint-Venant’s theory for beams with multi-connected cross-section: justification and error estimate. Zbl 1370.74087
Freddi, Lorenzo; Murat, François; Paroni, Roberto
2010
Stability by homogenization of thermoviscoplastic problems. Zbl 1253.74087
Charalambakis, Nicolas; Murat, Francois
2010
Two stable-by-homogenization models in simple shearing of rate-dependent non-homogeneous materials. Zbl 1425.74399
Charalambakis, Nicolas; Murat, François
2010
An elliptic problem with a lower order term having singular behaviour. Zbl 1173.35469
Giachetti, Daniela; Murat, François
2009
The div-curl lemma “trente ans après”: an extension and an application to the $$G$$-convergence of unbounded monotone operators. Zbl 1183.35012
Briane, M.; Casado-Díaz, J.; Murat, F.
2009
Homogenization of monotone operators in divergence form with $$x$$-dependent multivalued graphs. Zbl 1180.35077
Francfort, Gilles A.; Murat, François; Tartar, Luc
2009
Anisotropic inhomogeneous rectangular thin-walled beams. Zbl 1170.49014
Freddi, Lorenzo; Murat, François; Paroni, Roberto
2009
Homogenization of a pressurized tube made of elastoplastic materials with discontinuous properties. Zbl 1176.74147
Chatzigeorgiou, George; Charalambakis, Nicolas; Murat, Francois
2009
Global weak solutions to equations of motion for magnetic fluids. Zbl 1162.76408
Amirat, Youcef; Hamdache, Kamel; Murat, François
2008
Homogenization problems of a hollow cylinder made of elastic materials with discontinuous properties. Zbl 1169.74532
Chatzigeorgiou, George; Charalambakis, Nicolas; Murat, Francois
2008
The diffusion equation in a notched beam. Zbl 1136.35323
Casado-Díaz, Juan; Luna-Laynez, Manuel; Murat, François
2008
Semi-strong convergence of sequences satisfying a variational inequality. Zbl 1248.35088
Briane, Marc; Mokobodzki, Gabriel; Murat, François
2008
Junction of elastic plates and beams. Zbl 1133.35322
Gaudiello, Antonio; Monneau, Régis; Mossino, Jacqueline; Murat, François; Sili, Ali
2007
Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in $$L^1$$. Zbl 1144.65072
Casado-Díaz, J.; Chacón Rebollo, T.; Girault, V.; Gómez Mármol, M.; Murat, F.
2007
Uniqueness results for pseudomonotone problems with $$p>2$$. Zbl 1118.35307
Casado-Díaz, Juan; Murat, François; Porretta, Alessio
2007
Homogenization of stratified thermoviscoplastic materials. Zbl 1144.74364
Charalambakis, Nicolas; Murat, François
2006
Approximation by finite elements, existence and uniqueness for a model of stratified thermoviscoplastic materials. Zbl 1150.74046
Charalambakis, Nicolas; Murat, François
2006
Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms. Zbl 1149.35352
Grenon, Nathalie; Murat, François; Porretta, Alessio
2005
Uniqueness results for nonlinear elliptic equations with a lower order term. Zbl 1125.35343
Betta, M. Francesca; Mercaldo, Anna; Murat, François; Porzio, M. Michaela
2005
The Lewy–Stampacchia inequality for the obstacle problem with quadratic growth in the gradient. Zbl 1105.35041
Murat, F.; Mokrane, A.
2005
Variations on a strange semi-continuity result. Zbl 1081.47049
Briane, Marc; Mokobodzki, Gabriel; Murat, François
2005
Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains. Zbl 1110.35008
Dal Maso, Gianni; Murat, François
2004
Monotone operators in divergence form with $$X$$-dependent multivalued graphs. Zbl 1115.35047
Francfort, Gilles; Murat, François; Tatar, Luc
2004
The Lewy-Stampacchia inequality for bilateral problems. Zbl 1121.35066
Mokrane, Abdelhafid; Murat, François
2004
A model for two coupled turbulent fluids. III: Numerical approximation by finite elements. Zbl 1129.76326
Bernardi, C.; Chacón Rebollo, T.; Gómez Mármol, M.; Lewandowski, R.; Murat, F.
2004
Asymptotic behavior of diffusion problems in a domain made of two cylinders of different diameters and lengths. Zbl 1188.35058
Casado-Díaz, Juan; Luna-Laynez, Manuel; Murat, François
2004
Asymptotic behavior of an elastic beam fixed on a small part of one of its extremities. Zbl 1058.74047
Casado-Díaz, Juan; Luna-Laynez, Manuel; Murat, François
2004
Uniqueness of the Neumann condition and comparison results for Dirichlet pseudo-monotone problems. Zbl 1157.35363
Casado-Díaz, J.; Murat, F.; Porretta, A.
2004
Existence of renormalized solutions to nonlinear elliptic equations with lower-order terms and right-hand side a measure. Zbl 1165.35365
Betta, Maria Francesca; Mercaldo, Anna; Murat, François; Porzio, Maria Michaela
2003
On a turbulent system with unbounded eddy viscosities. Zbl 1013.35068
Gallouët, T.; Lederer, J.; Lewandowski, R.; Murat, F.; Tartar, L.
2003
A model for two coupled turbulent fluids. II: Numerical analysis of a spectral discretization. Zbl 1129.76327
Bernardi, C.; Chacón Rebollo, T.; Lewandowski, R.; Murat, F.
2003
A generalized strange term in Signorini’s type problems. Zbl 1040.35008
Conca, Carlos; Murat, François; Timofte, Claudia
2003
A chain rule formula for the composition of a vector-valued function by a piecewise smooth function. Zbl 1179.46037
Murat, François; Trombetti, Cristina
2003
Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in $$L^1(\Omega)$$. Zbl 1092.35032
Betta, M. F.; Mercaldo, A.; Murat, F.; Porzio, M. M.
2002
Stability properties, existence, and nonexistence of renormalized solutions for elliptic equations with measure data. Zbl 1129.35397
Murat, F.; Porretta, A.
2002
On the junction of elastic plates and beams. Zbl 1032.74037
Gaudiello, Antonio; Monneau, Régis; Mossino, Jacqueline; Murat, François; Sili, Ali
2002
Existence and uniqueness results for nonlinear elliptic problems with a lower order term and measure datum. Zbl 1016.35026
Betta, M. Francesca; Mercaldo, Anna; Murat, François; Porzio, M. Michaela
2002
A model for two coupled turbulent fluids. I: Analysis of the system. Zbl 1034.35106
Bernardi, C.; Chacón Rebollo, T.; Lewandowski, R.; Murat, F.
2002
Existence and uniqueness of a renormalized solution for a fairly general class of nonlinear parabolic problems. Zbl 0998.35030
Blanchard, Dominique; Murat, François; Redwane, Hicham
2001
Nonlinear problems having natural growth in the gradient: an existence result when the source terms are small. Zbl 1158.35358
Ferone, Vincenzo; Murat, François
2000
Nonlocal effects in the passage from 3d to 1d in linearized, anisotropic, heterogeneous elasticity. Zbl 0962.74009
Murat, François; Sili, Ali
2000
A model for two coupled turbulent fluids. Zbl 1009.76044
Bernardi, C.; Chacón Rebollo, T.; Lewandowski, R.; Murat, F.
2000
Renormalization solutions of elliptic equations with general measure data. Zbl 0958.35045
Dal Maso, Gianni; Murat, François; Orsina, Luigi; Prignet, Alain
1999
Asymptotic behavior of solutions of the anisotropic heterogeneous linearized elasticity system in thin cylinders. Zbl 0929.74010
Murat, François; Sili, Ali
1999
Existence and uniqueness of a renormalized solution for a fairly general nonlinear parabolic problem. Zbl 0935.35073
Blanchard, Dominique; Murat, François; Redwane, Hicham
1999
Existence of a solution for a model of two coupled turbulent fluids. Zbl 0930.35131
Bernardi, Christine; Chacon, Tomas; Lewandowski, Roger; Murat, François
1999
Almost everywhere convergence of gradients of solutions to nonlinear elliptic systems. Zbl 0890.35039
Dal Maso, Gianni; Murat, François
1998
Quasilinear problems having quadratic growth in the gradient: An existence result when the source term is small. Zbl 0917.35039
Ferone, Vincenzo; Murat, François
1998
A proof of the Lewy-Stampacchia’s inequality by a penalization method. Zbl 0918.35058
Mokrane, A.; Murat, F.
1998
Renormalised solutions of nonlinear parabolic problems with $$L^1$$ data: Existence and uniqueness. Zbl 0895.35050
Blanchard, D.; Murat, F.
1997
$$H$$-convergence. Zbl 0920.35019
Murat, François; Tartar, Luc
1997
A strange term coming from nowhere. Zbl 0912.35020
Cioranescu, Doina; Murat, François
1997
Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators. Zbl 0899.35007
Dal Maso, Gianni; Murat, François
1997
Definition and existence of renormalized solutions of elliptic equations with general measure data. Zbl 0887.35057
Dal Maso, Gianni; Murat, François; Orsina, Luigi; Prignet, Alain
1997
Calculus of variations and homogenization. Zbl 0939.35019
Murat, François; Tartar, Luc
1997
On the control of coefficients in partial differential equations. Zbl 0913.35020
Murat, François; Tartar, Luc
1997
A corrector result for $$H$$-converging parabolic problems with time-dependent coefficients. Zbl 1005.35015
Dall’Aglio, Andrea; Murat, François
1997
Quasilinear relaxed Dirichlet problems. Zbl 0863.35041
Finzi Vita, Stefano; Murat, François; Tchou, Nicoletta A.
1996
Definition and weak stability of nonconservative products. Zbl 0853.35068
Dal Maso, Gianni; LeFloch, Philippe G.; Murat, François
1995
Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions. Zbl 0859.35031
Barles, Guy; Murat, François
1995
Fourth-order moments of nonnegative measures on $$S^ 2$$ and applications. Zbl 0869.73006
Francfort, Gilles; Murat, François; Tartar, Luc
1995
Monotonous problems in cylinders consisting of heterogeneous material with vanishing diameter. Zbl 0833.35140
Murat, François; Sili, Ali
1995
The Stokes and Navier-Stokes equations with boundary conditions involving the pressure. Zbl 0826.35093
Conca, C.; Murat, F.; Pironneau, O.
1994
Dirichlet problems in perforated domains for homogeneous monotone operators on $$H_ 0^ 1$$. Zbl 0884.47026
Dal Maso, Gianni; Murat, François
1994
A property of nonlinear elliptic equations when the right-hand side is a measure. Zbl 0807.35034
Boccardo, Lucio; Murat, François
1994
Existence and regularity of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms. Zbl 0803.35046
Boccardo, L.; Giachetti, D.; Diaz, J. I.; Murat, F.
1993
Homogenization of the Neumann problem with nonisolated holes. Zbl 0823.35014
Allaire, Grégoire; Murat, François
1993
A unified presentation of two existence results for problems with natural growth. Zbl 0806.35033
Boccardo, L.; Gallouët, T.; Murat, F.
1993
Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations. Zbl 0783.35020
Boccardo, Lucio; Murat, François
1992
$$L^{\infty{}}$$ estimate for some nonlinear elliptic partial differential equations and application to an existence result. Zbl 0785.35033
Boccardo, L.; Murat, F.; Puel, J.-P.
1992
Correctors for the homogenization of the wave and heat equations. Zbl 0837.35016
Brahim-Otsmane, S.; Francfort, G. A.; Murat, F.
1992
Oscillations and energy densities in the wave equation. Zbl 0803.35010
Francfort, G. A.; Murat, F.
1992
Unicité de la solution de certaines équations elliptiques non linéaires. (Uniqueness of the solution of some nonlinear elliptic equations). Zbl 0789.35056
Boccardo, Lucio; Gallouët, Thierry; Murat, François
1992
$$H$$ convergence for quasi-linear elliptic equations with quadratic growth. Zbl 0795.35008
Bensoussan, A.; Boccardo, L.; Murat, F.
1992
On the optimality of certain Sobolev exponents for the weak continuity of determinants. Zbl 0769.46025
Dacorogna, B.; Murat, F.
1992
Homogenization of nonlinear unilateral problems. Zbl 0749.49009
Boccardo, Lucio; Murat, François
1991
Remarks on rank-one convexity and quasi convexity. Zbl 0751.49005
Ball, J. M.; Murat, F.
1991
Homogenization and corrector for the wave equation in domains with small holes. Zbl 0807.35077
Cioranescu, D.; Donato, P.; Murat, F.; Zuazua, E.
1991
Homogenization of renormalized solutions of elliptic equations. Zbl 0774.35007
Murat, François
1991
A generalization of a theorem of H.Brezis & F.E.Browder and applications to some unilateral problems. Zbl 0716.46032
Boccardo, L.; Giachetti, D.; Murat, F.
1990
Existence results for some quasilinear parabolic equations. Zbl 0705.35066
Boccardo, Lucio; Murat, François; Puel, Jean-Pierre
1989
Remarks on Chacon’s biting lemma. Zbl 0678.46023
Ball, J. M.; Murat, F.
1989
Existence of a solution for a weaker form of a nonlinear elliptic equation. Zbl 0703.35063
Boccardo, L.; Diaz, J. I.; Giachetti, D.; Murat, F.
1989
Weak solutions to the initial-boundary value problem for the shearing of non-homogeneous thermoviscoplastic materials. Zbl 0686.73007
Charalambakis, Nicolas; Murat, François
1989
...and 35 more Documents
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#### Cited by 2,586 Authors

 64 Murat, François 48 Boccardo, Lucio 45 Casado-Díaz, Juan 34 Coclite, Giuseppe Maria 28 Briane, Marc 28 Porretta, Alessio 27 Orsina, Luigi 26 Peral Alonso, Ireneo 25 Abdellaoui, Boumediene 24 Benkirane, Abdelmoujib 24 Dal Maso, Gianni 24 Mai Duc Thanh 24 Parés Madroñal, Carlos 23 Dumbser, Michael 22 Redwane, Hicham 21 Di Ruvo, Lorenzo 21 Martínez-Aparicio, Pedro J. 21 Pedregal, Pablo 20 Allaire, Grégoire 19 Arcoya, David 19 Blanchard, Dominique 19 Fonseca, Irene 18 Chen, Gui-Qiang G. 18 Sarrico, Carlos Orlando R. 17 Castro, Manuel J. 17 Klimsiak, Tomasz 17 LeFloch, Philippe Gerard 17 Mercaldo, Anna 16 Bennouna, Jaouad 16 Gaudiello, Antonio 16 Kogut, Peter I. 16 Lu, Yunguang 16 Müller, Stefan 16 Petitta, Francesco 16 Porzio, Maria Michaela 15 Giachetti, Daniela 14 Carmona Tapia, Jose 14 Guibé, Olivier 14 Segura de León, Sergio 13 Buttazzo, Giuseppe 13 Dall’Aglio, Andrea 13 Donato, Patrizia 12 Abdulle, Assyr 12 Betta, Maria Francesca 12 Castro-Díaz, Manuel Jesús 12 Conca, Carlos 12 Leonori, Tommaso 12 Mingione, Giuseppe 12 Paroni, Roberto 12 Rhoudaf, Mohamed 12 Visintin, Augusto 11 Azroul, Elhoussine 11 Bulíček, Miroslav 11 El Moumni, Mostafa 11 Fernández-Nieto, Enrique Domingo 11 Francfort, Gilles A. 11 Wittbold, Petra 10 Calvo-Jurado, Carmen 10 Conti, Sergio 10 Diaz Diaz, Jesus Ildefonso 10 Feireisl, Eduard 10 Gwiazda, Piotr 10 Luna-Laynez, Manuel 10 Milton, Graeme Walter 10 Nguyen Cong Phuc 10 Squassina, Marco 9 Amirat, Youcef Aït 9 Ball, John M. 9 Bidaut-Veron, Marie-Françoise 9 Cuong, Dao Huy 9 Gallouët, Thierry 9 Abreu Goncalves, Jose Valdo 9 Kohn, Robert Vita 9 Kovalevsky, Alexander Albertovich 9 Miyagaki, Olimpio Hiroshi 9 Oliva, Francescantonio 9 Panov, Evgeniy Yu. 9 Sciunzi, Berardino 9 Tağıyev, Rafiq Qäländär oğlu 9 Zou, Weilin 8 Abdellaoui, Mohammed Amin 8 Akdim, Youssef 8 Attar, Ahmed 8 Bendahmane, Mostafa 8 Braides, Andrea 8 Cao, Liqun 8 Chacón Rebollo, Tomás 8 Charalambakis, Nicolas Ch. 8 Chlebicka, Iwona 8 Damlamian, Alain 8 Frid, Hermano 8 Garroni, Adriana 8 Grabovsky, Yury 8 Hong, John Meng-Kai 8 Krömer, Stefan 8 Kuusi, Tuomo 8 Leonetti, Francesco 8 Lipton, Robert P. 8 Málek, Josef 8 Primo, Ana R. M. ...and 2,486 more Authors
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#### Cited in 314 Serials

 146 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 114 Journal of Mathematical Analysis and Applications 112 Journal of Differential Equations 106 Archive for Rational Mechanics and Analysis 84 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 67 Journal of Computational Physics 66 Calculus of Variations and Partial Differential Equations 62 Journal de Mathématiques Pures et Appliquées. Neuvième Série 59 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 55 Annali di Matematica Pura ed Applicata. Serie Quarta 53 Journal of Functional Analysis 52 Comptes Rendus. Mathématique. Académie des Sciences, Paris 47 Computer Methods in Applied Mechanics and Engineering 38 Nonlinear Analysis. Theory, Methods & Applications 34 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 32 Journal of the Mechanics and Physics of Solids 29 Computers and Fluids 29 SIAM Journal on Mathematical Analysis 27 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 26 Nonlinear Analysis. Real World Applications 25 NoDEA. Nonlinear Differential Equations and Applications 25 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 23 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 23 Ricerche di Matematica 22 Mathematics of Computation 21 Applied Mathematics and Computation 21 Journal of Elasticity 21 Journal of Mathematical Sciences (New York) 20 Applied Mathematics and Optimization 19 Applicable Analysis 19 Journal of Scientific Computing 19 Discrete and Continuous Dynamical Systems 19 Mediterranean Journal of Mathematics 19 Discrete and Continuous Dynamical Systems. Series S 18 Journal of Computational and Applied Mathematics 18 RAIRO. Modélisation Mathématique et Analyse Numérique 18 Communications in Partial Differential Equations 18 Advanced Nonlinear Studies 17 ZAMP. Zeitschrift für angewandte Mathematik und Physik 16 Communications in Mathematical Physics 16 Mathematics and Mechanics of Solids 16 Communications in Contemporary Mathematics 15 Applications of Mathematics 15 Journal of Evolution Equations 15 Complex Variables and Elliptic Equations 14 Manuscripta Mathematica 14 Transactions of the American Mathematical Society 13 Mathematical Methods in the Applied Sciences 13 Numerische Mathematik 13 Zeitschrift für Analysis und ihre Anwendungen 13 Applied Numerical Mathematics 13 Applied Mathematics Letters 13 Potential Analysis 12 Communications on Pure and Applied Analysis 11 Computers & Mathematics with Applications 11 Quarterly of Applied Mathematics 11 Acta Applicandae Mathematicae 11 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 11 Multiscale Modeling & Simulation 11 S$$\vec{\text{e}}$$MA Journal 10 International Journal of Engineering Science 10 Journal of Optimization Theory and Applications 10 SIAM Journal on Control and Optimization 10 Chinese Annals of Mathematics. Series B 10 Milan Journal of Mathematics 10 Structural and Multidisciplinary Optimization 10 Boundary Value Problems 10 Advances in Calculus of Variations 9 SIAM Journal on Numerical Analysis 9 Revista Matemática Iberoamericana 9 Abstract and Applied Analysis 9 Networks and Heterogeneous Media 8 Proceedings of the American Mathematical Society 8 SIAM Journal on Applied Mathematics 8 Journal of the European Mathematical Society (JEMS) 8 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 8 Boletim da Sociedade Paranaense de Matemática. Terceira Série 7 Journal d’Analyse Mathématique 7 Rendiconti del Circolo Matemàtico di Palermo. Serie II 7 Annales Mathématiques Blaise Pascal 7 Differential Equations 7 Journal of Fixed Point Theory and Applications 7 Advances in Nonlinear Analysis 7 Bollettino dell’Unione Matematica Italiana 6 Mathematical Notes 6 Nonlinearity 6 Monatshefte für Mathematik 6 Proceedings of the Japan Academy. Series A 6 Acta Mathematicae Applicatae Sinica. English Series 6 Asymptotic Analysis 6 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 6 Continuum Mechanics and Thermodynamics 6 Applicationes Mathematicae 6 Revista Matemática Complutense 6 Journal of Mathematical Fluid Mechanics 6 Acta Mathematica Sinica. English Series 6 Discrete and Continuous Dynamical Systems. Series B 5 Journal of Mathematical Physics 5 Advances in Mathematics 5 Rendiconti del Seminario Matematico della Università di Padova ...and 214 more Serials
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#### Cited in 49 Fields

 1,938 Partial differential equations (35-XX) 504 Fluid mechanics (76-XX) 478 Calculus of variations and optimal control; optimization (49-XX) 454 Mechanics of deformable solids (74-XX) 308 Numerical analysis (65-XX) 169 Functional analysis (46-XX) 117 Operator theory (47-XX) 57 Global analysis, analysis on manifolds (58-XX) 53 Probability theory and stochastic processes (60-XX) 52 Potential theory (31-XX) 50 Statistical mechanics, structure of matter (82-XX) 48 Optics, electromagnetic theory (78-XX) 45 Classical thermodynamics, heat transfer (80-XX) 41 Real functions (26-XX) 41 Biology and other natural sciences (92-XX) 28 Systems theory; control (93-XX) 25 Measure and integration (28-XX) 25 Harmonic analysis on Euclidean spaces (42-XX) 25 Operations research, mathematical programming (90-XX) 22 Ordinary differential equations (34-XX) 20 Geophysics (86-XX) 15 Integral equations (45-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Functions of a complex variable (30-XX) 10 Dynamical systems and ergodic theory (37-XX) 10 Differential geometry (53-XX) 10 Mechanics of particles and systems (70-XX) 8 Quantum theory (81-XX) 7 Several complex variables and analytic spaces (32-XX) 7 Astronomy and astrophysics (85-XX) 6 Approximations and expansions (41-XX) 6 General topology (54-XX) 6 Information and communication theory, circuits (94-XX) 5 Computer science (68-XX) 4 General and overarching topics; collections (00-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Convex and discrete geometry (52-XX) 4 Relativity and gravitational theory (83-XX) 3 History and biography (01-XX) 3 Difference and functional equations (39-XX) 3 Algebraic topology (55-XX) 2 Number theory (11-XX) 2 Topological groups, Lie groups (22-XX) 2 Abstract harmonic analysis (43-XX) 2 Manifolds and cell complexes (57-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 1 Statistics (62-XX)