Edit Profile (opens in new tab) Murat, François Co-Author Distance Author ID: murat.francois Published as: Murat, François; Murat, F.; Murat, Francois more...less Homepage: https://www.ljll.math.upmc.fr/membres/fiches/murat.html External Links: MGP · Wikidata · dblp Documents Indexed: 159 Publications since 1971, including 2 Additional arXiv Preprints 5 Contributions as Editor Co-Authors: 89 Co-Authors with 151 Joint Publications 2,392 Co-Co-Authors all top 5 Co-Authors 13 single-authored 24 Boccardo, Lucio 12 Casado-Díaz, Juan 10 Giachetti, Daniela 9 Puel, Jean-Pierre 9 Sili, Ali 8 Chacón Rebollo, Tomás 8 Charalambakis, Nicolas Ch. 8 Francfort, Gilles A. 7 Dal Maso, Gianni 7 Tartar, Luc C. 6 Bernardi, Christine 6 Lewandowski, Roger 6 Martínez-Aparicio, Pedro J. 6 Mercaldo, Anna 6 Mokrane, Abdelhafid 6 Porretta, Alessio 5 Betta, Maria Francesca 5 Girault, Vivette 5 Mignot, Fulbert 5 Porzio, Maria Michaela 4 Bensoussan, Alain 4 Cioranescu, Doina 4 Conca, Carlos 4 Gaudiello, Antonio 4 Luna-Laynez, Manuel 4 Pironneau, Olivier 3 Ball, John MacLeod 3 Blanchard, Dominique 3 Briane, Marc 3 Chatzigeorgiou, George 3 Ferone, Vincenzo 3 Gallouët, Thierry 3 Gómez Mármol, Macarena 3 Haraux, Alain 3 Joseph, Anthony 3 Monneau, Régis 3 Mossino, Jacqueline 3 Paroni, Roberto 3 Prum, Bernard 3 Rentschler, Rudolf 2 Bègue, Catherine 2 Brahim-Otsmane, Safia 2 Díaz Díaz, Jesús Ildefonso 2 Farroni, Fernando 2 Freddi, Lorenzo 2 Grenon, Nathalie 2 Lions, Jacques-Louis 2 Mokobodzki, Gabriel 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 Petitta, Francesco 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 all top 5 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 1 Mathematics in Engineering all top 5 Fields 130 Partial differential equations (35-XX) 28 Calculus of variations and optimal control; optimization (49-XX) 26 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 Functions of a complex variable (30-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Geophysics (86-XX) 2 Systems theory; control (93-XX) 1 Combinatorics (05-XX) 1 Ordinary differential equations (34-XX) 1 Sequences, series, summability (40-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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 141 Publications have been cited 5,832 times in 3,768 Documents Cited by ▼ Year ▼ Definition and weak stability of nonconservative products. Zbl 0853.35068 Dal Maso, Gianni; LeFloch, Philippe G.; Murat, François 429 1995 Compacite par compensation. Zbl 0399.46022 Murat, Francois 334 1978 Renormalization solutions of elliptic equations with general measure data. Zbl 0958.35045 Dal Maso, Gianni; Murat, François; Orsina, Luigi; Prignet, Alain 330 1999 Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations. Zbl 0783.35020 Boccardo, Lucio; Murat, François 297 1992 \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals. Zbl 0549.46019 Ball, J. M.; Murat, F. 250 1984 Existence of bounded solutions for non linear elliptic unilateral problems. Zbl 0687.35042 Boccardo, L.; Murat, F.; Puel, J. P. 205 1988 \(H\)-convergence. Zbl 0920.35019 Murat, François; Tartar, Luc 177 1997 Renormalised solutions of nonlinear parabolic problems with \(L^1\) data: Existence and uniqueness. Zbl 0895.35050 Blanchard, D.; Murat, F. 163 1997 Un terme etrange venu d’ailleurs. Zbl 0496.35030 Cioranescu, D.; Murat, F. 132 1982 \(L^{\infty{}}\) estimate for some nonlinear elliptic partial differential equations and application to an existence result. Zbl 0785.35033 Boccardo, L.; Murat, F.; Puel, J.-P. 131 1992 Homogenization and optimal bounds in linear elasticity. Zbl 0604.73013 Francfort, G. A.; Murat, F. 120 1986 The embedding of the positive cone of \(H^{-1}\) in \(W^{-1,\,q}\) is compact for all \(q<2\) (with a remark of Haim Brezis). (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 120 1981 Compacite par compensation: condition necessaire et suffisante de continuite faible sous une hypothèse de rang constant. Zbl 0464.46034 Murat, Francois 118 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 111 2001 On a nonlinear partial differential equation having natural growth terms and unbounded solution. Zbl 0696.35042 Bensoussan, A.; Boccardo, L.; Murat, F. 102 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. 97 1993 The Stokes and Navier-Stokes equations with boundary conditions involving the pressure. Zbl 0826.35093 Conca, C.; Murat, F.; Pironneau, O. 90 1994 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. 88 1984 A strange term coming from nowhere. Zbl 0912.35020 Cioranescu, Doina; Murat, François 84 1997 Correctors for the homogenization of the wave and heat equations. Zbl 0837.35016 Brahim-Otsmane, S.; Francfort, G. A.; Murat, F. 82 1992 Étude de problèmes d’optimal design. Zbl 0334.49013 Murat, Francois; Simon, Jacques 82 1976 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. 80 1983 Existence de solutions non bornées pour certaines équations quasi- linéaires. Zbl 0524.35041 Boccardo, L.; Murat, F.; Puel, J. P. 78 1982 Nonlinear problems having natural growth in the gradient: an existence result when the source terms are small. Zbl 1158.35358 Ferone, Vincenzo; Murat, François 76 2000 Remarks on Chacon’s biting lemma. Zbl 0678.46023 Ball, J. M.; Murat, F. 65 1989 Existence results for some quasilinear parabolic equations. Zbl 0705.35066 Boccardo, Lucio; Murat, François; Puel, Jean-Pierre 64 1989 Almost everywhere convergence of gradients of solutions to nonlinear elliptic systems. Zbl 0890.35039 Dal Maso, Gianni; Murat, François 61 1998 Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions. Zbl 0859.35031 Barles, Guy; Murat, François 59 1995 Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators. Zbl 0899.35007 Dal Maso, Gianni; Murat, François 53 1997 Contre-exemples pour divers problèmes ou le contrôle intervient dans les coefficients. Zbl 0349.49005 Murat, Francois 52 1977 Homogenization of the Neumann problem with nonisolated holes. Zbl 0823.35014 Allaire, Grégoire; Murat, François 43 1993 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. 41 1988 A priori estimates and existence for elliptic equations with gradient dependent terms. Zbl 1305.35058 Grenon, Nathalie; Murat, François; Porretta, Alessio 40 2014 An elliptic problem with a lower order term having singular behaviour. Zbl 1173.35469 Giachetti, Daniela; Murat, François 38 2009 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 38 2017 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 36 2003 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 35 1997 Quasilinear problems having quadratic growth in the gradient: An existence result when the source term is small. Zbl 0917.35039 Ferone, Vincenzo; Murat, François 35 1998 Calculus of variations and homogenization. Zbl 0939.35019 Murat, François; Tartar, Luc 34 1997 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. 34 2002 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 34 1971 Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms. Zbl 1149.35352 Grenon, Nathalie; Murat, François; Porretta, Alessio 33 2005 Optimality conditions and homogenization. Zbl 0569.49015 Murat, F.; Tartar, L. 32 1985 Oscillations and energy densities in the wave equation. Zbl 0803.35010 Francfort, G. A.; Murat, F. 32 1992 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. 31 1989 Global weak solutions to equations of motion for magnetic fluids. Zbl 1162.76408 Amirat, Youcef; Hamdache, Kamel; Murat, François 31 2008 Asymptotic behavior of solutions of the anisotropic heterogeneous linearized elasticity system in thin cylinders. (Comportement asymptotique des solutions du système de l’élasticité linéarisée anisotrope hétérogène dans des cylindres minces.) Zbl 0929.74010 Murat, François; Sili, Ali 30 1999 Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains. Zbl 1110.35008 Dal Maso, Gianni; Murat, François 30 2004 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 29 1992 The Neumann sieve. Zbl 0586.35037 Murat, F. 28 1985 Remarques sur l’homogénéisation de certains problèmes quasi- linéaires. Zbl 0524.35042 Boccardo, Lucio; Murat, François 27 1982 Existence and uniqueness of a renormalized solution for a fairly general nonlinear parabolic problem. (Existence et unicité de la solution renormalisée d’un problème parabolique non linéaire assez général.) Zbl 0935.35073 Blanchard, Dominique; Murat, François; Redwane, Hicham 27 1999 Junction of elastic plates and beams. Zbl 1133.35322 Gaudiello, Antonio; Monneau, Régis; Mossino, Jacqueline; Murat, François; Sili, Ali 26 2007 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 26 2018 Homogenization of the brush problem with a source term in \(L^{1}\). Zbl 1371.35067 Gaudiello, Antonio; Guibé, Olivier; Murat, François 26 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 25 2005 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 23 1987 Variation d’un point de retournement par rapport au domaine. Zbl 0422.35039 Mignot, F.; Murat, F.; Puel, J. P. 23 1979 Stability properties, existence, and nonexistence of renormalized solutions for elliptic equations with measure data. Zbl 1129.35397 Murat, F.; Porretta, A. 23 2002 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. 22 2009 On a turbulent system with unbounded eddy viscosities. Zbl 1013.35068 Gallouët, T.; Lederer, J.; Lewandowski, R.; Murat, F.; Tartar, L. 22 2003 A unified presentation of two existence results for problems with natural growth. Zbl 0806.35033 Boccardo, L.; Gallouët, T.; Murat, F. 21 1993 Un terme etrange venu d’ailleurs. II. Zbl 0498.35034 Cioranescu, Doina; Murat, Francois 21 1982 Nonlinear elliptic equations with natural growth in the gradient and source terms in Lorentz spaces. Zbl 1318.35031 Ferone, Vincenzo; Murat, François 21 2014 Quelques propriétés des opérateurs elliptiques quasi linéaires. (Some properties of quasilinear elliptic operators). Zbl 0696.35050 Boccardo, Lucio; Murat, François; Puel, Jean-Pierre 20 1988 Compacite par compensation II. Zbl 0427.35008 Murat, F. 19 1979 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. 19 2007 On the junction of elastic plates and beams. Zbl 1032.74037 Gaudiello, Antonio; Monneau, Régis; Mossino, Jacqueline; Murat, François; Sili, Ali 19 2002 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. 19 2003 \(H\) convergence for quasi-linear elliptic equations with quadratic growth. Zbl 0795.35008 Bensoussan, A.; Boccardo, L.; Murat, F. 18 1992 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 17 1972 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 17 2018 Nouveaux résultats de convergence dans des problèmes unilateraux. Zbl 0484.49009 Boccardo, L.; Murat, F. 16 1982 Monotonous problems in cylinders consisting of heterogeneous material with vanishing diameter. (Problèmes monotones dans des cylindres de faible diamètre formés de matériaux hétérogènes.) Zbl 0833.35140 Murat, François; Sili, Ali 15 1995 Monotone operators in divergence form with \(X\)-dependent multivalued graphs. Zbl 1115.35047 Francfort, Gilles; Murat, François; Tatar, Luc 15 2004 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 15 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. 15 2002 Fourth-order moments of nonnegative measures on \(S^ 2\) and applications. Zbl 0869.73006 Francfort, Gilles; Murat, François; Tartar, Luc 14 1995 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. 14 1986 Homogenization problems of a hollow cylinder made of elastic materials with discontinuous properties. Zbl 1169.74532 Chatzigeorgiou, George; Charalambakis, Nicolas; Murat, Francois 13 2008 A generalized strange term in Signorini’s type problems. Zbl 1040.35008 Conca, Carlos; Murat, François; Timofte, Claudia 13 2003 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. 13 2004 Homogenization of nonlinear unilateral problems. Zbl 0749.49009 Boccardo, Lucio; Murat, François 12 1991 On the optimality of certain Sobolev exponents for the weak continuity of determinants. Zbl 0769.46025 Dacorogna, B.; Murat, F. 12 1992 A property of nonlinear elliptic equations when the right-hand side is a measure. Zbl 0807.35034 Boccardo, Lucio; Murat, François 12 1994 Estimation de L’erreur dans des problèmes de Dirichlet ou apparat un terme étrange. (Error estimates in a Dirichlet problem where a strange term appears). Zbl 0687.35007 Kacimi, Hayat; Murat, François 12 1989 Analysis of a coupled fluid-structure model with applications to hemodynamics. Zbl 1343.35184 Chacón Rebollo, T.; Girault, V.; Murat, F.; Pironneau, O. 11 2016 Homogenization of renormalized solutions of elliptic equations. Zbl 0774.35007 Murat, François 10 1991 Homogenization of monotone operators in divergence form with \(x\)-dependent multivalued graphs. Zbl 1180.35077 Francfort, Gilles A.; Murat, François; Tartar, Luc 10 2009 Uniqueness results for pseudomonotone problems with \(p>2\). Zbl 1118.35307 Casado-Díaz, Juan; Murat, François; Porretta, Alessio 10 2007 Nonlocal effects in the passage from 3d to 1d in linearized, anisotropic, heterogeneous elasticity. (Effets non locaux dans le passage 3d-1d en élasticité linéairisée anisotrope hétérogène.) Zbl 0962.74009 Murat, François; Sili, Ali 10 2000 On the control of coefficients in partial differential equations. Zbl 0913.35020 Murat, François; Tartar, Luc 9 1997 A proof of the Lewy-Stampacchia’s inequality by a penalization method. Zbl 0918.35058 Mokrane, A.; Murat, F. 9 1998 Weak solutions to the initial-boundary value problem for the shearing of non-homogeneous thermoviscoplastic materials. Zbl 0686.73007 Charalambakis, Nicolas; Murat, François 9 1989 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 9 2018 Remarks on rank-one convexity and quasi convexity. Zbl 0751.49005 Ball, J. M.; Murat, F. 8 1991 Homogenization and corrector for the wave equation in domains with small holes. Zbl 0807.35077 Cioranescu, D.; Donato, P.; Murat, F.; Zuazua, E. 8 1991 The Lewy–Stampacchia inequality for the obstacle problem with quadratic growth in the gradient. Zbl 1105.35041 Murat, F.; Mokrane, A. 8 2005 Optimal bounds for conduction in two-dimensional, two-phase, anisotropic media. Zbl 0668.73018 Francfort, G. A.; Murat, F. 8 1987 The Lewy-Stampacchia inequality for bilateral problems. Zbl 1121.35066 Mokrane, Abdelhafid; Murat, François 8 2004 Semilinear problems with right-hand sides singular at \(u=0\) which change sign. Zbl 1466.35111 Casado-Díaz, Juan; Murat, François 3 2021 The ergodic limit for weak solutions of elliptic equations with Neumann boundary condition. Zbl 1497.35220 Murat, François; Porretta, Alessio 1 2021 A remark about the periodic homogenization of certain composite fibered media. Zbl 1441.35028 Murat, François; Sili, Ali 5 2020 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 26 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 17 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 9 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 6 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. 4 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 38 2017 Homogenization of the brush problem with a source term in \(L^{1}\). Zbl 1371.35067 Gaudiello, Antonio; Guibé, Olivier; Murat, François 26 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. 3 2017 Analysis of a coupled fluid-structure model with applications to hemodynamics. Zbl 1343.35184 Chacón Rebollo, T.; Girault, V.; Murat, F.; Pironneau, O. 11 2016 Advances in the study of singular semilinear elliptic problems. Zbl 1403.35109 Giachetti, Daniela; Martínez-Aparicio, Pedro J.; Murat, François 5 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 4 2016 A priori estimates and existence for elliptic equations with gradient dependent terms. Zbl 1305.35058 Grenon, Nathalie; Murat, François; Porretta, Alessio 40 2014 Nonlinear elliptic equations with natural growth in the gradient and source terms in Lorentz spaces. Zbl 1318.35031 Ferone, Vincenzo; Murat, François 21 2014 Lewy-Stampacchia’s inequality for a Leray-Lions operator with natural growth in the gradient. Zbl 1301.49025 Mokrane, A.; Murat, F. 2 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 1 2014 Homogenization and correctors for monotone problems in cylinders of small diameter. Zbl 1288.35040 Casado-Díaz, Juan; Murat, François; Sili, Ali 4 2013 An example of a functional which is weakly lower semicontinuous on \(W_0^{1,p}\) for every \(p>2\) but not on \(H_0^1\). Zbl 1211.49015 Farroni, Fernando; Giova, Raffaella; Murat, François 1 2011 Finite element discretization of Darcy’s equations with pressure-dependent porosity. Zbl 1271.76166 Girault, Vivette; Murat, François; Salgado, Abner 7 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 4 2010 Stability by homogenization of thermoviscoplastic problems. Zbl 1253.74087 Charalambakis, Nicolas; Murat, Francois 3 2010 Two stable-by-homogenization models in simple shearing of rate-dependent non-homogeneous materials. Zbl 1425.74399 Charalambakis, Nicolas; Murat, François 3 2010 An elliptic problem with a lower order term having singular behaviour. Zbl 1173.35469 Giachetti, Daniela; Murat, François 38 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. 22 2009 Homogenization of monotone operators in divergence form with \(x\)-dependent multivalued graphs. Zbl 1180.35077 Francfort, Gilles A.; Murat, François; Tartar, Luc 10 2009 Anisotropic inhomogeneous rectangular thin-walled beams. Zbl 1170.49014 Freddi, Lorenzo; Murat, François; Paroni, Roberto 7 2009 Homogenization of a pressurized tube made of elastoplastic materials with discontinuous properties. Zbl 1176.74147 Chatzigeorgiou, George; Charalambakis, Nicolas; Murat, Francois 2 2009 Global weak solutions to equations of motion for magnetic fluids. Zbl 1162.76408 Amirat, Youcef; Hamdache, Kamel; Murat, François 31 2008 Homogenization problems of a hollow cylinder made of elastic materials with discontinuous properties. Zbl 1169.74532 Chatzigeorgiou, George; Charalambakis, Nicolas; Murat, Francois 13 2008 The diffusion equation in a notched beam. Zbl 1136.35323 Casado-Díaz, Juan; Luna-Laynez, Manuel; Murat, François 7 2008 On the notions of solution to nonlinear elliptic problems: results and developments. Zbl 1203.35007 4 2008 Semi-strong convergence of sequences satisfying a variational inequality. Zbl 1248.35088 Briane, Marc; Mokobodzki, Gabriel; Murat, François 3 2008 Junction of elastic plates and beams. Zbl 1133.35322 Gaudiello, Antonio; Monneau, Régis; Mossino, Jacqueline; Murat, François; Sili, Ali 26 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. 19 2007 Uniqueness results for pseudomonotone problems with \(p>2\). Zbl 1118.35307 Casado-Díaz, Juan; Murat, François; Porretta, Alessio 10 2007 Homogenization of stratified thermoviscoplastic materials. Zbl 1144.74364 Charalambakis, Nicolas; Murat, François 8 2006 Approximation by finite elements, existence and uniqueness for a model of stratified thermoviscoplastic materials. Zbl 1150.74046 Charalambakis, Nicolas; Murat, François 5 2006 Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms. Zbl 1149.35352 Grenon, Nathalie; Murat, François; Porretta, Alessio 33 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 25 2005 The Lewy–Stampacchia inequality for the obstacle problem with quadratic growth in the gradient. Zbl 1105.35041 Murat, F.; Mokrane, A. 8 2005 Variations on a strange semi-continuity result. Zbl 1081.47049 Briane, Marc; Mokobodzki, Gabriel; Murat, François 2 2005 Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains. Zbl 1110.35008 Dal Maso, Gianni; Murat, François 30 2004 Monotone operators in divergence form with \(X\)-dependent multivalued graphs. Zbl 1115.35047 Francfort, Gilles; Murat, François; Tatar, Luc 15 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. 13 2004 The Lewy-Stampacchia inequality for bilateral problems. Zbl 1121.35066 Mokrane, Abdelhafid; Murat, François 8 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 7 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 6 2004 Uniqueness of the Neumann condition and comparison results for Dirichlet pseudo-monotone problems. Zbl 1157.35363 Casado-Díaz, J.; Murat, F.; Porretta, A. 1 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 36 2003 On a turbulent system with unbounded eddy viscosities. Zbl 1013.35068 Gallouët, T.; Lederer, J.; Lewandowski, R.; Murat, F.; Tartar, L. 22 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. 19 2003 A generalized strange term in Signorini’s type problems. Zbl 1040.35008 Conca, Carlos; Murat, François; Timofte, Claudia 13 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 8 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. 34 2002 Stability properties, existence, and nonexistence of renormalized solutions for elliptic equations with measure data. Zbl 1129.35397 Murat, F.; Porretta, A. 23 2002 On the junction of elastic plates and beams. Zbl 1032.74037 Gaudiello, Antonio; Monneau, Régis; Mossino, Jacqueline; Murat, François; Sili, Ali 19 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 15 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. 15 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 111 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 76 2000 Nonlocal effects in the passage from 3d to 1d in linearized, anisotropic, heterogeneous elasticity. (Effets non locaux dans le passage 3d-1d en élasticité linéairisée anisotrope hétérogène.) Zbl 0962.74009 Murat, François; Sili, Ali 10 2000 A model for two coupled turbulent fluids. Zbl 1009.76044 Bernardi, C.; Chacón Rebollo, T.; Lewandowski, R.; Murat, F. 1 2000 Renormalization solutions of elliptic equations with general measure data. Zbl 0958.35045 Dal Maso, Gianni; Murat, François; Orsina, Luigi; Prignet, Alain 330 1999 Asymptotic behavior of solutions of the anisotropic heterogeneous linearized elasticity system in thin cylinders. (Comportement asymptotique des solutions du système de l’élasticité linéarisée anisotrope hétérogène dans des cylindres minces.) Zbl 0929.74010 Murat, François; Sili, Ali 30 1999 Existence and uniqueness of a renormalized solution for a fairly general nonlinear parabolic problem. (Existence et unicité de la solution renormalisée d’un problème parabolique non linéaire assez général.) Zbl 0935.35073 Blanchard, Dominique; Murat, François; Redwane, Hicham 27 1999 Existence of a solution for a model of two coupled turbulent fluids. (Existence d’une solution pour un modèle de deux fluides turbulents couplés.) Zbl 0930.35131 Bernardi, Christine; Chacon, Tomas; Lewandowski, Roger; Murat, François 1 1999 Almost everywhere convergence of gradients of solutions to nonlinear elliptic systems. Zbl 0890.35039 Dal Maso, Gianni; Murat, François 61 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 35 1998 A proof of the Lewy-Stampacchia’s inequality by a penalization method. Zbl 0918.35058 Mokrane, A.; Murat, F. 9 1998 Renormalized solutions of nonlinear elliptic equations with measure data. (Équations elliptiques non linéaires monotones avec un deuxième membre \(L^1\) ou mesure.) Zbl 1213.35230 Murat, François 2 1998 \(H\)-convergence. Zbl 0920.35019 Murat, François; Tartar, Luc 177 1997 Renormalised solutions of nonlinear parabolic problems with \(L^1\) data: Existence and uniqueness. Zbl 0895.35050 Blanchard, D.; Murat, F. 163 1997 A strange term coming from nowhere. Zbl 0912.35020 Cioranescu, Doina; Murat, François 84 1997 Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators. Zbl 0899.35007 Dal Maso, Gianni; Murat, François 53 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 35 1997 Calculus of variations and homogenization. Zbl 0939.35019 Murat, François; Tartar, Luc 34 1997 On the control of coefficients in partial differential equations. Zbl 0913.35020 Murat, François; Tartar, Luc 9 1997 A corrector result for \(H\)-converging parabolic problems with time-dependent coefficients. Zbl 1005.35015 Dall’Aglio, Andrea; Murat, François 8 1997 Quasilinear relaxed Dirichlet problems. Zbl 0863.35041 Finzi Vita, Stefano; Murat, François; Tchou, Nicoletta A. 2 1996 Definition and weak stability of nonconservative products. Zbl 0853.35068 Dal Maso, Gianni; LeFloch, Philippe G.; Murat, François 429 1995 Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions. Zbl 0859.35031 Barles, Guy; Murat, François 59 1995 Monotonous problems in cylinders consisting of heterogeneous material with vanishing diameter. (Problèmes monotones dans des cylindres de faible diamètre formés de matériaux hétérogènes.) Zbl 0833.35140 Murat, François; Sili, Ali 15 1995 Fourth-order moments of nonnegative measures on \(S^ 2\) and applications. Zbl 0869.73006 Francfort, Gilles; Murat, François; Tartar, Luc 14 1995 The Stokes and Navier-Stokes equations with boundary conditions involving the pressure. Zbl 0826.35093 Conca, C.; Murat, F.; Pironneau, O. 90 1994 A property of nonlinear elliptic equations when the right-hand side is a measure. Zbl 0807.35034 Boccardo, Lucio; Murat, François 12 1994 Dirichlet problems in perforated domains for homogeneous monotone operators on \(H_ 0^ 1\). Zbl 0884.47026 Dal Maso, Gianni; Murat, François 7 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. 97 1993 Homogenization of the Neumann problem with nonisolated holes. Zbl 0823.35014 Allaire, Grégoire; Murat, François 43 1993 A unified presentation of two existence results for problems with natural growth. Zbl 0806.35033 Boccardo, L.; Gallouët, T.; Murat, F. 21 1993 Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations. Zbl 0783.35020 Boccardo, Lucio; Murat, François 297 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. 131 1992 Correctors for the homogenization of the wave and heat equations. Zbl 0837.35016 Brahim-Otsmane, S.; Francfort, G. A.; Murat, F. 82 1992 Oscillations and energy densities in the wave equation. Zbl 0803.35010 Francfort, G. A.; Murat, F. 32 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 29 1992 \(H\) convergence for quasi-linear elliptic equations with quadratic growth. Zbl 0795.35008 Bensoussan, A.; Boccardo, L.; Murat, F. 18 1992 On the optimality of certain Sobolev exponents for the weak continuity of determinants. Zbl 0769.46025 Dacorogna, B.; Murat, F. 12 1992 Homogenization of nonlinear unilateral problems. Zbl 0749.49009 Boccardo, Lucio; Murat, François 12 1991 Homogenization of renormalized solutions of elliptic equations. Zbl 0774.35007 Murat, François 10 1991 ...and 41 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,451 Authors 65 Murat, François 61 Boccardo, Lucio 57 Casado-Díaz, Juan 42 Coclite, Giuseppe Maria 37 Redwane, Hicham 35 Benkirane, Abdelmoujib 34 Mai Duc Thanh 33 Briane, Marc 33 Orsina, Luigi 31 Parés Madroñal, Carlos 30 Dumbser, Michael 29 Porretta, Alessio 28 Lu, Yunguang 27 Abdellaoui, Boumediene 27 Bennouna, Jaouad 27 Dal Maso, Gianni 27 Peral Alonso, Ireneo 26 Allaire, Grégoire 26 Di Ruvo, Lorenzo 25 Chen, Gui-Qiang G. 24 Sarrico, Carlos Orlando R. 23 Martínez-Aparicio, Pedro J. 23 Pedregal, Pablo 22 Mercaldo, Anna 21 Arcoya, David 21 Castro, Manuel J. 21 Guibé, Olivier 20 Azroul, Elhoussine 20 Fonseca, Irene 19 Akdim, Youssef 19 Blanchard, Dominique 19 Gaudiello, Antonio 19 Petitta, Francesco 19 Porzio, Maria Michaela 19 Segura de León, Sergio 18 Bulíček, Miroslav 18 Donato, Patrizia 18 El Moumni, Mostafa 18 Klimsiak, Tomasz 18 Kogut, Peter I. 18 LeFloch, Philippe Gerard 18 Shaposhnikova, Tatiana Ardolionovna 17 Abdellaoui, Mohammed Amin 17 Buttazzo, Giuseppe 17 Conca, Carlos 17 Giachetti, Daniela 16 Carmona Tapia, Jose 16 Müller, Stefan 16 Rhoudaf, Mohamed 15 Abdulle, Assyr 15 Betta, Maria Francesca 15 Bidaut-Veron, Marie-Françoise 15 Castro-Díaz, Manuel Jesús 15 Dall’Aglio, Andrea 15 Díaz Díaz, Jesús Ildefonso 15 Oliva, Francescantonio 14 Francfort, Gilles A. 14 Leonori, Tommaso 14 Nguyen Cong Phuc 14 Véron, Laurent 13 Calvo-Jurado, Carmen 13 Cuong, Dao Huy 13 Gwiazda, Piotr 13 Kovalevsky, Alexander Albertovich 13 Luna-Laynez, Manuel 13 Sili, Ali 13 Toro, Eleuterio Francisco 13 Visintin, Augusto 12 Conti, Sergio 12 El Hadfi, Youssef 12 Feireisl, Eduard 12 Fernández-Nieto, Enrique Domingo 12 Gil, Antonio J. 12 Málek, Josef 12 Milton, Graeme Walter 12 Ortigosa, Rogelio 12 Paroni, Roberto 11 Chlebicka, Iwona 11 Abreu Goncalves, Jose Valdo 11 Grabovsky, Yury 11 Jouve, François 11 Klingenberg, Christian 11 Marah, Amine 11 Mingione, Giuseppe 11 Rindler, Filip 11 Schweizer, Ben 11 Sciunzi, Berardino 11 Sun, Meina 11 Wittbold, Petra 10 Aberqi, Ahmed 10 Amirat, Youcef Aït 10 Ball, John MacLeod 10 Bendahmane, Mostafa 10 Berthon, Christophe 10 Bressan, Alberto 10 Gallouët, Thierry 10 Hjiaj, Hassane 10 Kurganov, Alexander 10 Lipton, Robert P. 10 Miyagaki, Olimpio Hiroshi ...and 3,351 more Authors all top 5 Cited in 414 Serials 160 Nonlinear Analysis. 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Series B 9 Bollettino dell’Unione Matematica Italiana 8 Nonlinearity 8 Advances in Mathematics 8 International Journal for Numerical Methods in Engineering 8 Proceedings of the American Mathematical Society ...and 314 more Serials all top 5 Cited in 48 Fields 2,823 Partial differential equations (35-XX) 778 Fluid mechanics (76-XX) 642 Mechanics of deformable solids (74-XX) 632 Calculus of variations and optimal control; optimization (49-XX) 501 Numerical analysis (65-XX) 228 Functional analysis (46-XX) 171 Operator theory (47-XX) 72 Probability theory and stochastic processes (60-XX) 71 Optics, electromagnetic theory (78-XX) 71 Statistical mechanics, structure of matter (82-XX) 68 Classical thermodynamics, heat transfer (80-XX) 65 Global analysis, analysis on manifolds (58-XX) 64 Potential theory (31-XX) 63 Biology and other natural sciences (92-XX) 58 Real functions (26-XX) 47 Systems theory; control (93-XX) 45 Measure and integration (28-XX) 39 Operations research, mathematical programming (90-XX) 35 Harmonic analysis on Euclidean spaces (42-XX) 35 Geophysics (86-XX) 32 Ordinary differential equations (34-XX) 21 Differential geometry (53-XX) 20 Integral equations (45-XX) 17 Functions of a complex variable (30-XX) 17 Dynamical systems and ergodic theory (37-XX) 17 Mechanics of particles and systems (70-XX) 17 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 16 Quantum theory (81-XX) 11 Relativity and gravitational theory (83-XX) 11 Astronomy and astrophysics (85-XX) 9 Several complex variables and analytic spaces (32-XX) 9 Approximations and expansions (41-XX) 9 General topology (54-XX) 9 Computer science (68-XX) 8 Information and communication theory, circuits (94-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 5 General and overarching topics; collections (00-XX) 5 Convex and discrete geometry (52-XX) 4 History and biography (01-XX) 3 Topological groups, Lie groups (22-XX) 3 Difference and functional equations (39-XX) 3 Algebraic topology (55-XX) 2 Commutative algebra (13-XX) 2 Abstract harmonic analysis (43-XX) 2 Manifolds and cell complexes (57-XX) 2 Statistics (62-XX) 1 Number theory (11-XX) 1 Category theory; homological algebra (18-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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