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## Caffarelli, Luis Ángel

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 Author ID: caffarelli.luis-a Published as: Caffarelli, Luis A.; Caffarelli, Luis; Caffarelli, L. A.; Caffarelli, L.; Caffarelli, Luis Ángel; Cafferelli, L. A. Homepage: http://www.ma.utexas.edu/users/caffarel/ External Links: MGP · ORCID · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND · IdRef Awards: Wolf Prize (2012) · Shaw Prize (2018)
 Documents Indexed: 308 Publications since 1974, including 8 Books Biographic References: 1 Publication
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#### Co-Authors

 58 single-authored 43 Friedman, Avner 18 Nirenberg, Louis 13 Spruck, Joel 12 Alt, Hans Wilhelm 12 Athanasopoulos, Ioannis 11 Salsa, Sandro 10 Silvestre, Luis E. 8 Mellet, Antoine 8 Vazquez, Juan Luis 6 Li, YanYan 6 Markowich, Peter Alexander 6 Sire, Yannick 6 Vasseur, Alexis F. 5 Berestycki, Henri 5 Kenig, Carlos Eduardo 5 Lee, Ki-Ahm 5 Lin, Fang Hua 5 Riviere, Nestor M. 5 Roquejoffre, Jean-Michel 5 Savin, Ovidiu V. 5 Shahgholian, Henrik 5 Valdinoci, Enrico 4 Aronson, Donald G. 4 Cabré, Xavier 4 Córdoba Barba, Antonio Juan 4 Crandall, Michael G. 4 Figalli, Alessio 4 Gutiérrez, Cristian E. 4 Souganidis, Panagiotis E. 4 Wang, Lihe 4 Wolanski, Noemi I. 3 Aguilera, Néstor E. 3 Arapostathis, Aristotle 3 Burger, Martin 3 De Silva, Daniela 3 Huang, Qingbo 3 Jerison, David S. 3 Wolfram, Marie-Therese 2 Allen, Mark G. 2 Ambrosio, Luigi 2 Biswas, Anup 2 Bjorland, Clayton 2 Bonforte, Matteo 2 Calderón, Calixto Pedro 2 de la Llave, Rafael 2 Fabes, Eugene B. 2 Gidas, Basilis 2 Grillo, Gabriele 2 Karakhanyan, Aram L. 2 Kohn, Robert Vita 2 Lederman, Claudia B. 2 McCann, Robert J. 2 Milakis, Emmanouil 2 Milman, Mario Marcos 2 Oliker, Vladimir I. 2 Patrizi, Stefania 2 Quitalo, Veronica 2 Salazar, Jorge A. 2 Stinga, Pablo Raúl 2 Torelli, Alessandro 2 Urbano, José Miguel 1 Brenier, Yann 1 Brézis, Haïm 1 Brezzi, Franco 1 Buttazzo, Giuseppe 1 Cagnetti, Filippo 1 Chan, Chi Hin 1 Charro, Fernando 1 Dávila, Gonzalo 1 Dipierro, Serena 1 Dolbeault, Jean 1 E, Weinan 1 Feldman, Mikhail 1 Garofalo, Nicola 1 Gilardi, Gianni 1 Glowinski, Roland 1 González, María del Mar 1 Gualdani, Maria Pia 1 Guan, Pengfei 1 Hardt, Robert M. 1 Jin, Tianling 1 Kamin, Shoshana 1 Karp, Lavi 1 Kinderlehrer, David 1 Kocan, Maciej 1 Kochengin, Sergey A. 1 Kohn, Joseph J. 1 Kriventsov, Dennis 1 Leitão, Raimundo A. 1 Lieb, Elliott H. 1 Littman, Walter 1 Ma, Xi-Nan 1 Manasevich, Raul F. 1 Maugeri, Antonino 1 Monneau, Régis 1 Mortola, Stefano 1 Muler, Nora E. 1 Nguyen, Truyen Van 1 Pang, Guodong 1 Peral Alonso, Ireneo ...and 26 more Co-Authors
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#### Serials

 35 Communications on Pure and Applied Mathematics 21 Archive for Rational Mechanics and Analysis 21 Indiana University Mathematics Journal 18 Communications in Partial Differential Equations 12 Annals of Mathematics. Second Series 10 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 8 Transactions of the American Mathematical Society 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Advances in Mathematics 5 Duke Mathematical Journal 5 Journal of Differential Equations 5 Journal für die Reine und Angewandte Mathematik 5 Proceedings of the American Mathematical Society 5 Journal of the American Mathematical Society 4 American Journal of Mathematics 4 Calculus of Variations and Partial Differential Equations 4 Discrete and Continuous Dynamical Systems 3 Communications in Mathematical Physics 3 Acta Mathematica 3 Inventiones Mathematicae 3 Revista Matemática Iberoamericana 3 Differential and Integral Equations 3 SIAM Journal on Mathematical Analysis 3 Journal of the European Mathematical Society (JEMS) 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Pacific Journal of Mathematics 2 SIAM Journal on Control and Optimization 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Communications in Analysis and Geometry 2 Journal of Mathematical Sciences (New York) 2 St. Petersburg Mathematical Journal 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Fixed Point Theory and Applications 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Rocky Mountain Journal of Mathematics 1 Studia Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Calcolo 1 Colloquium Mathematicum 1 Compositio Mathematica 1 Illinois Journal of Mathematics 1 Journal of Functional Analysis 1 Manuscripta Mathematica 1 Mathematische Annalen 1 RAIRO. Analyse Numérique 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Chinese Annals of Mathematics. Series B 1 Journal of Scientific Computing 1 The Journal of Geometric Analysis 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the National Academy of Sciences of the United States of America 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Bollettino della Unione Matemàtica Italiana. Serie VII. B 1 Journal of Partial Differential Equations 1 Journal of Dynamics and Differential Equations 1 Topological Methods in Nonlinear Analysis 1 The Journal of Fourier Analysis and Applications 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Interfaces and Free Boundaries 1 Journal of Numerical Mathematics 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Communications in Mathematical Sciences 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Bollettino della Unione Matematica Italiana. Series V. A 1 Bulletin of the American Mathematical Society 1 Colloquium Publications. American Mathematical Society 1 Contemporary Mathematics 1 Graduate Studies in Mathematics 1 Lecture Notes in Mathematics 1 IAS/Park City Mathematics Series 1 Networks and Heterogeneous Media 1 Discrete and Continuous Dynamical Systems. Series S 1 Kinetic and Related Models 1 Annals of PDE 1 Philosophical Transactions A. Royal Society of London
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#### Fields

 255 Partial differential equations (35-XX) 68 Calculus of variations and optimal control; optimization (49-XX) 42 Fluid mechanics (76-XX) 17 Differential geometry (53-XX) 16 Potential theory (31-XX) 12 Operator theory (47-XX) 11 Global analysis, analysis on manifolds (58-XX) 11 Mechanics of deformable solids (74-XX) 10 Classical thermodynamics, heat transfer (80-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 General and overarching topics; collections (00-XX) 8 Optics, electromagnetic theory (78-XX) 7 Real functions (26-XX) 7 Functional analysis (46-XX) 7 Numerical analysis (65-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Probability theory and stochastic processes (60-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Integral equations (45-XX) 4 History and biography (01-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Systems theory; control (93-XX) 3 Measure and integration (28-XX) 3 Quantum theory (81-XX) 2 Ordinary differential equations (34-XX) 2 Convex and discrete geometry (52-XX) 2 Operations research, mathematical programming (90-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

271 Publications have been cited 13,618 times in 7,901 Documents Cited by Year
An extension problem related to the fractional Laplacian. Zbl 1143.26002
Caffarelli, Luis; Silvestre, Luis
2007
Partial regularity of suitable weak solutions of the Navier-Stokes equations. Zbl 0509.35067
Caffarelli, L.; Kohn, R.; Nirenberg, Louis
1982
Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Zbl 0702.35085
Caffarelli, Luis A.; Gidas, Basilis; Spruck, Joel
1989
Fully nonlinear elliptic equations. Zbl 0834.35002
Caffarelli, Luis A.; Cabré, Xavier
1995
First order interpolation inequalities with weights. Zbl 0563.46024
Caffarelli, L.; Kohn, R.; Nirenberg, Louis
1984
Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063
Caffarelli, Luis A.; Vasseur, Alexis
2010
The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian. Zbl 0654.35031
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1985
Existence and regularity for a minimum problem with free boundary. Zbl 0449.35105
Alt, H. W.; Caffarelli, L. A.
1981
Interior a priori estimates for solutions of fully nonlinear equations. Zbl 0692.35017
Caffarelli, Luis A.
1989
On $$W^{1,p}$$ estimates for elliptic equations in divergence form. Zbl 0906.35030
Caffarelli, L. A.; Peral, I.
1998
Regularity theory for fully nonlinear integro-differential equations. Zbl 1170.45006
Caffarelli, Luis; Silvestre, Luis
2009
The Dirichlet problem for nonlinear second-order elliptic equations. I: Monge-Ampère equation. Zbl 0598.35047
Caffarelli, L.; Nirenberg, Louis; Spruck, J.
1984
Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Zbl 1148.35097
Caffarelli, Luis A.; Salsa, Sandro; Silvestre, Luis
2008
Interior $$W^{2,p}$$ estimates for solutions of the Monge-Ampère equation. Zbl 0704.35044
Caffarelli, Luis A.
1990
Variational problems with two phases and their free boundary. Zbl 0844.35137
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
1984
Nonlocal minimal surfaces. Zbl 1248.53009
Caffarelli, L.; Roquejoffre, J.-M.; Savin, O.
2010
The obstacle problem revisited. Zbl 0928.49030
Caffarelli, L. A.
1998
Non-local diffusions, drifts and games. Zbl 1266.35060
Caffarelli, Luis
2012
A geometric approach to free boundary problems. Zbl 1083.35001
Caffarelli, Luis; Salsa, Sandro
2005
Boundary behavior of nonnegative solutions of elliptic operators in divergence form. Zbl 0512.35038
Caffarelli, L.; Fabes, E.; Mortola, S.; Salsa, S.
1981
The regularity of free boundaries in higher dimensions. Zbl 0386.35046
Caffarelli, Luis A.
1978
On viscosity solutions of fully nonlinear equations with measurable ingredients. Zbl 0854.35032
Caffarelli, L.; Crandall, M. G.; Kocan, M.; Świȩch, A.
1996
A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity. Zbl 0704.35045
Caffarelli, L. A.
1990
Further qualitative properties for elliptic equations in unbounded domains. Zbl 1079.35513
Berestycki, Henri; Caffarelli, Luis; Nirenberg, Louis
1997
Variational problems with free boundaries for the fractional Laplacian. Zbl 1221.35453
Caffarelli, Luis A.; Roquejoffre, Jean-Michel; Sire, Yannick
2010
The Dirichlet problem for nonlinear second-order elliptic equations. II: Complex Monge-Ampère, and uniformly elliptic, equations. Zbl 0598.35048
Caffarelli, L.; Kohn, J. J.; Nirenberg, Louis; Spruck, J.
1985
Monotonicity for elliptic equations in unbounded Lipschitz domains. Zbl 0906.35035
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1997
The regularity of mappings with a convex potential. Zbl 0753.35031
Caffarelli, Luis A.
1992
Vortex condensation in the Chern-Simons Higgs model: An existence theorem. Zbl 0846.58063
Caffarelli, Luis A.; Yang, Yisong
1995
Regularity results for nonlocal equations by approximation. Zbl 1231.35284
Caffarelli, Luis; Silvestre, Luis
2011
Some regularity properties of solutions of Monge Ampère equation. Zbl 0761.35028
Caffarelli, Luis A.
1991
A Harnack inequality approach to the regularity of free boundaries. II: Flat free boundaries are Lipschitz. Zbl 0676.35086
Caffarelli, Luis A.
1989
A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are $$C^{1,\alpha}$$. Zbl 0676.35085
Caffarelli, Luis A.
1987
Convexity of solutions of semilinear elliptic equations. Zbl 0599.35065
Caffarelli, Luis A.; Friedman, Avner
1985
Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105
Caffarelli, Luis; Vazquez, Juan Luis
2011
Convexity properties of solutions to some classical variational problems. Zbl 0508.49013
Caffarelli, Luis A.; Spruck, Joel
1982
The initial trace of a solution of the porous medium equation. Zbl 0556.76084
Aronson, D. G.; Caffarelli, L. A.
1983
Fractional elliptic equations, Caccioppoli estimates and regularity. Zbl 1381.35211
Caffarelli, Luis A.; Stinga, Pablo Raúl
2016
Inequalities for second-order elliptic equations with applications to unbounded domains. I. Zbl 0860.35004
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1996
Boundary regularity of maps with convex potentials. II. Zbl 0916.35016
Caffarelli, Luis A.
1996
Properties of the solutions of the linearized Monge-Ampère equation. Zbl 0878.35039
Caffarelli, Luis A.; Gutiérrez, Cristian E.
1997
A parabolic problem with a fractional time derivative. Zbl 1338.35428
Allen, Mark; Caffarelli, Luis; Vasseur, Alexis
2016
Uniform estimates and limiting arguments for nonlocal minimal surfaces. Zbl 1357.49143
Caffarelli, Luis; Valdinoci, Enrico
2011
Regularity of the free boundary of a gas flow in an $$n$$-dimensional porous medium. Zbl 0439.76085
Caffarelli, Luis A.; Friedman, Avner
1980
Boundary regularity of maps with convex potentials. Zbl 0778.35015
Caffarelli, Luis A.
1992
Nonlinear second-order elliptic equations. V: The Dirichlet problem for Weingarten hypersurfaces. Zbl 0672.35028
Caffarelli, Luis; Nirenberg, Louis; Spruck, Joel
1988
The Evans-Krylov theorem for nonlocal fully nonlinear equations. Zbl 1232.49043
Caffarelli, Luis; Silvestre, Luis
2011
Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098
Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis
2011
Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs. Zbl 1053.49032
Caffarelli, Luis A.; Feldman, Mikhail; McCann, Robert J.
2002
Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. Zbl 1194.35138
Caffarelli, L. A.; Lin, Fang-Hua
2008
Continuity of the temperature in the two-phase Stefan problem. Zbl 0516.35080
Caffarelli, L. A.; Evans, L. C.
1983
Regularity of a free boundary with application to the Pompeiu problem. Zbl 0960.35112
Caffarelli, Luis A.; Karp, Lavi; Shahgholian, Henrik
2000
A Harnack inequality approach to the regularity of free boundaries. III: Existence theory, compactness, and dependence on X. Zbl 0702.35249
Caffarelli, Luis A.
1988
Further regularity for the Signorini problem. Zbl 0427.35019
Caffarelli, L. A.
1979
Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media. Zbl 1063.35025
Caffarelli, Luis A.; Souganidis, Panagiotis E.; Wang, L.
2005
Lipschitz continuity of solutions and interfaces of the N-dimensional porous medium equation. Zbl 0644.35058
Caffarelli, L. A.; Vazquez, J. L.; Wolanski, N. I.
1987
Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations. Zbl 0593.35047
Caffarelli, Luis A.; Friedman, Avner
1985
Monotonicity properties of optimal transportation and the FKG and related inequalities. Zbl 0978.60107
Caffarelli, Luis A.
2000
An extension to a theorem of Jörgens, Calabi, and Pogorelov. Zbl 1236.35041
Caffarelli, L.; Li, YanYan
2003
Uniform estimates for regularization of free boundary problems. Zbl 0702.35252
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1990
A free boundary problem for quasi-linear elliptic equations. Zbl 0554.35129
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
1984
An $$L^ \infty$$ bound for solutions of the Cahn-Hilliard equation. Zbl 0851.35010
Caffarelli, Luis A.; Muler, Nora E.
1995
An optimal partition problem for eigenvalues. Zbl 1123.65060
Cafferelli, L. A.; Lin, Fang Hua
2007
Optimal transportation and applications. Lectures given at the C. I. M. E. summer school, Martina Franca, Italy, September 2–8, 2001. Zbl 1013.00028
Ambrosio, Luigi; Brenier, Yann; Buttazzo, Giusseppe; Caffarelli, Luis A.; Salsa, S. (ed.); Villani, Cédric
2003
A free-boundary problem for the heat equation arising in flame propagation. Zbl 0814.35149
Caffarelli, Luis A.; Vázquez, Juan L.
1995
Some new monotonicity theorems with applications to free boundary problems. Zbl 1142.35382
Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E.
2002
Uniform convergence of a singular perturbation problem. Zbl 0829.49013
Caffarelli, Luis A.; Córdoba, Antonio
1995
Global energy minimizers for free boundary problems and full regularity in three dimensions. Zbl 1330.35545
Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E.
2004
The structure of the free boundary for lower dimensional obstacle problems. Zbl 1185.35339
Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S.
2008
Completely singular elliptic-harmonic measures. Zbl 0482.35020
Caffarelli, Luis A.; Fabes, Eugene B.; Kenig, Carlos E.
1981
Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312
Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis
2013
The obstacle problem for the biharmonic operator. Zbl 0405.31007
Caffarelli, Luis A.; Friedman, Avner
1979
Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278
Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio
2012
Non-local gradient dependent operators. Zbl 1252.35099
Bjorland, C.; Caffarelli, L.; Figalli, A.
2012
Compactness methods in free boundary problems. Zbl 0437.35070
Caffarelli, Luis A.
1980
Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088
Caffarelli, Luis; Figalli, Alessio
2013
A gradient bound for entire solutions of quasi-linear equations and its consequences. Zbl 0819.35016
Caffarelli, Luis; Garofalo, Nicola; Segala, Fausto
1994
Continuity of the density of a gas flow in a porous medium. Zbl 0425.35060
Caffarelli, Luis A.; Friedman, Avner
1979
Regularity properties of nonlocal minimal surfaces via limiting arguments. Zbl 1284.53008
Caffarelli, Luis; Valdinoci, Enrico
2013
Free boundaries in optimal transport and Monge-Ampère obstacle problems. Zbl 1196.35231
Caffarelli, Luis A.; McCann, Robert J.
2010
Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043
Caffarelli, Luis; Vázquez, Juan-Luis
2011
Rates of convergence for the homogenization of fully nonlinear uniformly elliptic PDE in random media. Zbl 1192.35048
Caffarelli, Luis A.; Souganidis, Panagiotis E.
2010
Symmetry for elliptic equations in a half space. Zbl 0793.35034
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1993
Real analysis related to the Monge-Ampère equation. Zbl 0858.35034
Caffarelli, Luis A.; Gutiérrez, Cristian E.
1996
An optimization problem with volume constraint. Zbl 0588.49005
Aguilera, N.; Alt, H. W.; Caffarelli, L. A.
1986
Regularity of a free boundary in parabolic potential theory. Zbl 1054.35142
Caffarelli, Luis; Petrosyan, Arshak; Shahgholian, Henrik
2004
The blow-up boundary for nonlinear wave equations. Zbl 0638.35053
Caffarelli, Luis A.; Friedman, Avner
1986
Allocation maps with general cost functions. Zbl 0883.49030
Caffarelli, Luis A.
1996
Optimal regularity of lower dimensional obstacle problems. Zbl 1108.35038
Athanasopoulos, I.; Caffarelli, L. A.
2004
Planelike minimizers in periodic media. Zbl 1036.49040
Caffarelli, Luis A.; de la Llave, Rafael
2001
How an initially stationary interface begins to move in porous medium flow. Zbl 0542.76119
Aronson, D. G.; Caffarelli, L. A.; Kamin, S.
1983
Nonlinear second order elliptic equations. IV. Starshaped compact Weingarten hypersurfaces. Zbl 0672.35027
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1986
Potential methods in variational inequalities. Zbl 0455.49010
Caffarelli, L. A.; Kinderlehrer, D.
1980
Regularity of the free boundary in parabolic phase-transition problems. Zbl 0891.35164
Athanasopoulos, I.; Caffarelli, L.; Salsa, S.
1996
Smoothness and analyticity of free boundaries in variational inequalities. Zbl 0363.35009
Caffarelli, L. A.; Riviere, N. M.
1976
Continuity of the temperature in boundary heat control problems. Zbl 1190.35125
Athanasopoulos, I.; Caffarelli, L. A.
2010
Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems. Zbl 0853.35049
Athanasopoulos, I.; Caffarelli, L.; Salsa, S.
1996
Asymptotic estimates for the plasma problem. Zbl 0466.35033
Caffarelli, Luis A.; Friedman, Avner
1980
On the case of equality in the Brunn-Minkowski inequality for capacity. Zbl 0847.31005
Caffarelli, Luis A.; Jerison, David; Lieb, Elliott H.
1996
Regularity of the free boundary for the one-dimensional flow of gas in a porous medium. Zbl 0439.76084
Caffarelli, Luis A.; Friedman, Avner
1979
Regularity for $$C^{1, \alpha}$$ interface transmission problems. Zbl 1467.35169
Caffarelli, Luis Ángel; Soria-Carro, María; Stinga, Pablo Raúl
2021
Minimal surfaces and free boundaries: recent developments. Zbl 1433.35464
Caffarelli, Luis A.; Sire, Yannick
2020
Fully nonlinear integro-differential equations with deforming kernels. Zbl 1452.35055
Caffarelli, Luis; Teymurazyan, Rafayel; Urbano, José Miguel
2020
Optimal regularity and structure of the free boundary for minimizers in cohesive zone models. Zbl 1442.49005
Caffarelli, L.; Cagnetti, F.; Figalli, A.
2020
Existence of weak solutions to a continuity equation with space time nonlocal Darcy law. Zbl 1459.35233
Caffarelli, Luis; Gualdani, Maria; Zamponi, Nicola
2020
Parabolic obstacle problems, quasi-convexity and regularity. Zbl 1432.35264
Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil
2019
Ergodic control of a class of jump diffusions with finite Lévy measures and rough kernels. Zbl 1415.93288
Arapostathis, Ari; Caffarelli, Luis; Pang, Guodong; Zheng, Yi
2019
On uniqueness of solutions to viscous HJB equations with a subquadratic nonlinearity in the gradient. Zbl 1428.35125
Arapostathis, Ari; Biswas, Anup; Caffarelli, Luis
2019
Interior regularity for fractional systems. Zbl 1411.35111
Caffarelli, Luis; Dávila, Gonzalo
2019
On the regularity of the non-dynamic parabolic fractional obstacle problem. Zbl 1394.35588
Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil
2018
A minimization problem with free boundary related to a cooperative system. Zbl 1395.35226
Caffarelli, Luis A.; Shahgholian, Henrik; Yeressian, Karen
2018
Bounds on the Green function for integral operators and fractional harmonic measure with applications to boundary Harnack. Zbl 1387.35071
Caffarelli, Luis A.; Sire, Yannick
2018
Two-phase anisotropic free boundary problems and applications to the Bellman equation in 2D. Zbl 1393.35247
Caffarelli, L.; De Silva, D.; Savin, O.
2018
Obstacle problems for integro-differential operators: regularity of solutions and free boundaries. Zbl 1371.35361
Caffarelli, Luis; Ros-Oton, Xavier; Serra, Joaquim
2017
Porous medium flow with both a fractional potential pressure and fractional time derivative. Zbl 1372.35328
Allen, Mark; Caffarelli, Luis; Vasseur, Alexis
2017
On some pointwise inequalities involving nonlocal operators. Zbl 06703883
Caffarelli, Luis A.; Sire, Yannick
2017
A logistic equation with nonlocal interactions. Zbl 1356.35261
Caffarelli, Luis; Dipierro, Serena; Valdinoci, Enrico
2017
The two membranes problem for different operators. Zbl 1368.35045
Caffarelli, L.; De Silva, D.; Savin, O.
2017
On a long range segregation model. Zbl 1386.35084
Caffarelli, L.; Patrizi, S.; Quitalo, V.
2017
Fractional elliptic equations, Caccioppoli estimates and regularity. Zbl 1381.35211
Caffarelli, Luis A.; Stinga, Pablo Raúl
2016
A parabolic problem with a fractional time derivative. Zbl 1338.35428
Allen, Mark; Caffarelli, Luis; Vasseur, Alexis
2016
A free boundary problem related to thermal insulation. Zbl 1351.35268
Caffarelli, Luis A.; Kriventsov, Dennis
2016
Obstacle-type problems for minimal surfaces. Zbl 1370.35070
Caffarelli, L.; De Silva, D.; Savin, O.
2016
The Dirichlet problem for stable-like operators and related probabilistic representations. Zbl 1352.60080
Arapostathis, Ari; Biswas, Anup; Caffarelli, Luis
2016
Regularity of solutions of the fractional porous medium flow with exponent $$1/2$$. Zbl 1335.35273
Caffarelli, L.; Vázquez, J. L.
2016
A non-local Monge-Ampère equation. Zbl 1361.35067
Caffarelli, Luis; Silvestre, Luis
2016
Minimization of a fractional perimeter-Dirichlet integral functional. Zbl 1323.35216
Caffarelli, Luis; Savin, Ovidiu; Valdinoci, Enrico
2015
On a fractional Monge-Ampère operator. Zbl 1393.35268
Caffarelli, Luis; Charro, Fernando
2015
Regularity of free boundaries a heuristic retro. Zbl 1353.35319
Caffarelli, Luis A.; Shahgholian, Henrik
2015
A bifurcation phenomenon in a singularly perturbed one-phase free boundary problem of phase transition. Zbl 1334.35439
Caffarelli, Luis A.; Wang, Peiyong
2015
Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities. Zbl 1296.35208
Caffarelli, Luis; Jin, Tianling; Sire, Yannick; Xiong, Jingang
2014
Partial differential equation models in the socio-economic sciences. Zbl 1353.00004
Burger, Martin; Caffarelli, Luis; Markowich, Peter A.
2014
Hölder regularity for generalized master equations with rough kernels. Zbl 1312.45013
Caffarelli, Luis; Silvestre, Luis
2014
On the asymptotic behavior of a Boltzmann-type price formation model. Zbl 1307.35302
Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese
2014
Regularity for anisotropic fully nonlinear integro-differential equations. Zbl 1304.35730
Caffarelli, Luis A.; Leitão, Raimundo; Urbano, José Miguel
2014
Counter-example in three dimension and homogenization of geometric motions in two dimension. Zbl 1293.35026
Caffarelli, L. A.; Monneau, R.
2014
A perturbation argument for a Monge-Ampère type equation arising in optimal transportation. Zbl 1294.35170
Caffarelli, Luis; Del Mar González, María; Nguyen, Truyen
2014
Relations between geometric convexity, doubling measures and property $$\Gamma$$. Zbl 1307.46006
Caffarelli, Luis A.; Crandall, Michael G.
2014
Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312
Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis
2013
Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088
Caffarelli, Luis; Figalli, Alessio
2013
Regularity properties of nonlocal minimal surfaces via limiting arguments. Zbl 1284.53008
Caffarelli, Luis; Valdinoci, Enrico
2013
Some remarks on singular solutions of nonlinear elliptic equations. III: Viscosity solutions including parabolic operators. Zbl 1279.35044
Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis
2013
On a Boltzmann-type price formation model. Zbl 1372.91039
Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese
2013
A priori bounds for solutions of a nonlocal evolution PDE. Zbl 1273.35067
Caffarelli, Luis; Valdinoci, Enrico
2013
Non-local diffusions, drifts and games. Zbl 1266.35060
Caffarelli, Luis
2012
Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278
Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio
2012
Non-local gradient dependent operators. Zbl 1252.35099
Bjorland, C.; Caffarelli, L.; Figalli, A.
2012
Some remarks on singular solutions of nonlinear elliptic equations. II: Symmetry and monotonicity via moving planes. Zbl 1325.35044
Caffarelli, Luis; Li, YanYan; Nirenberg, Louis
2012
Traveling waves for a boundary reaction-diffusion equation. Zbl 1255.35072
Caffarelli, L.; Mellet, A.; Sire, Y.
2012
The De Giorgi method for nonlocal fluid dynamics. Zbl 1357.35249
Caffarelli, Luis A.; Vasseur, Alexis
2012
The problem of two sticks. Zbl 1257.46009
Caffarelli, Luis A.; Crandall, Michael G.
2012
Regularity results for nonlocal equations by approximation. Zbl 1231.35284
Caffarelli, Luis; Silvestre, Luis
2011
Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105
Caffarelli, Luis; Vazquez, Juan Luis
2011
Uniform estimates and limiting arguments for nonlocal minimal surfaces. Zbl 1357.49143
Caffarelli, Luis; Valdinoci, Enrico
2011
The Evans-Krylov theorem for nonlocal fully nonlinear equations. Zbl 1232.49043
Caffarelli, Luis; Silvestre, Luis
2011
Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098
Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis
2011
Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043
Caffarelli, Luis; Vázquez, Juan-Luis
2011
On a price formation free boundary model by Lasry and Lions. Zbl 1216.91012
Caffarelli, Luis A.; Markowich, Peter A.; Pietschmann, Jan-F.
2011
On a price formation free boundary model by Lasry and Lions: the Neumann problem. Zbl 1233.91336
Caffarelli, Luis A.; Markowich, Peter A.; Wolfram, Marie-Therese
2011
Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063
Caffarelli, Luis A.; Vasseur, Alexis
2010
Nonlocal minimal surfaces. Zbl 1248.53009
Caffarelli, L.; Roquejoffre, J.-M.; Savin, O.
2010
Variational problems with free boundaries for the fractional Laplacian. Zbl 1221.35453
Caffarelli, Luis A.; Roquejoffre, Jean-Michel; Sire, Yannick
2010
Free boundaries in optimal transport and Monge-Ampère obstacle problems. Zbl 1196.35231
Caffarelli, Luis A.; McCann, Robert J.
2010
Rates of convergence for the homogenization of fully nonlinear uniformly elliptic PDE in random media. Zbl 1192.35048
Caffarelli, Luis A.; Souganidis, Panagiotis E.
2010
Continuity of the temperature in boundary heat control problems. Zbl 1190.35125
Athanasopoulos, I.; Caffarelli, L. A.
2010
Convergence of nonlocal threshold dynamics approximations to front propagation. Zbl 1190.65132
Caffarelli, Luis A.; Souganidis, Panagiotis E.
2010
The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Zbl 1210.76039
Caffarelli, Luis A.; Vasseur, Alexis F.
2010
Distance functions and almost global solutions of eikonal equations. Zbl 1187.35024
Caffarelli, Luis A.; Crandall, Michael G.
2010
Analysis on the junctions of domain walls. Zbl 1193.35255
Caffarelli, Luis A.; Lin, Fang Hua
2010
On the Evans-Krylov theorem. Zbl 1180.35229
Caffarelli, Luis; Silvestre, Luis
2010
Smooth approximations of solutions to nonconvex fully nonlinear elliptic equations. Zbl 1208.35047
Caffarelli, Luis; Silvestre, Luis
2010
Regularity theory for fully nonlinear integro-differential equations. Zbl 1170.45006
Caffarelli, Luis; Silvestre, Luis
2009
Some remarks on singular solutions of nonlinear elliptic equations. I. Zbl 1215.35068
Caffarelli, Luis; Li, Yan Yan; Nirenberg, Louis
2009
The geometry of solutions to a segregation problem for nondivergence systems. Zbl 1217.35015
Caffarelli, L. A.; Karakhanyan, A. L.; Lin, Fang-Hua
2009
Nonlocal heat flows preserving the $$L^2$$ energy. Zbl 1154.35364
Caffarelli, Luis; Lin, Fanghua
2009
Random homogenization of an obstacle problem. Zbl 1180.35069
Caffarelli, L. A.; Mellet, A.
2009
Surfaces minimizing nonlocal energies. Zbl 1182.53055
Caffarelli, Luis A.
2009
Reflector problem in $${\mathbb R^n}$$ endowed with non-Euclidean norm. Zbl 1173.78003
Caffarelli, Luis A.; Huang, Qingbo
2009
Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Zbl 1148.35097
Caffarelli, Luis A.; Salsa, Sandro; Silvestre, Luis
2008
Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. Zbl 1194.35138
Caffarelli, L. A.; Lin, Fang-Hua
2008
The structure of the free boundary for lower dimensional obstacle problems. Zbl 1185.35339
Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S.
2008
A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs. Zbl 1140.65075
Caffarelli, Luis A.; Souganidis, Panagiotis E.
2008
Weak solutions of one inverse problem in geometric optics. Zbl 1202.78003
Caffarelli, L. A.; Oliker, V. I.
2008
On the regularity of reflector antennas. Zbl 1140.35009
Caffarelli, Luis A.; Gutiíerrez, Cristian E.; Huang, Qingbo
2008
Random homogenization of fractional obstacle problems. Zbl 1156.74359
Caffarelli, Luis; Mellet, Antoine
2008
A counterexample to $$C^{2,1}$$ regularity for parabolic fully nonlinear equations. Zbl 1162.35042
Caffarelli, Luis A.; Stefanelli, Ulisse
2008
Numerical solution of the Dirichlet problem for a Pucci equation in dimension two. Application to homogenization. Zbl 1155.65097
Caffarelli, L. A.; Glowinski, R.
2008
Viscosity method for homogenization of highly oscillating obstacles. Zbl 1158.35109
Caffarelli, Luis; Lee, Ki-Ahm
2008
Some nonlinear problems involving nonlocal diffusions. Zbl 1419.35203
Caffarelli, Luis A.
2008
An extension problem related to the fractional Laplacian. Zbl 1143.26002
Caffarelli, Luis; Silvestre, Luis
2007
An optimal partition problem for eigenvalues. Zbl 1123.65060
Cafferelli, L. A.; Lin, Fang Hua
2007
A constant rank theorem for solutions of fully nonlinear elliptic equations. Zbl 1191.35127
Caffarelli, Luis A.; Guan, Pengfei; Ma, Xinan
2007
Uniform Hölder estimates in a class of elliptic systems and applications to singular limits in models for diffusion flames. Zbl 1189.35084
Caffarelli, Luis A.; Roquejoffre, Jean-Michel
2007
Capillary drops: contact angle hysteresis and sticking drops. Zbl 1168.76007
Caffarelli, L. A.; Mellet, A.
2007
Capillary drops on an inhomogeneous surface. Zbl 1200.76053
Caffarelli, L. A.; Mellet, A.
2007
Homogenization of oscillating free boundaries: the elliptic case. Zbl 1122.35156
Caffarelli, L.; Lee, K.
2007
Flame propagation in one-dimensional stationary ergodic media. Zbl 1110.76054
Caffarelli, L. A.; Lee, K.-A.; Mellet, A.
2007
Free boundary problems for fractional powers of the Laplacian. Zbl 1253.35224
Caffarelli, Luis
2007
Phase transitions: uniform regularity of the intermediate layers. Zbl 1090.49019
Caffarelli, Luis A.; Córdoba, Antonio
2006
Homogenization and flame propagation in periodic excitable media: the asymptotic speed of propagation. Zbl 1093.35010
Caffarelli, L. A.; Lee, K.-A.; Mellet, A.
2006
...and 171 more Documents
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#### Cited by 5,645 Authors

 121 Caffarelli, Luis Ángel 102 Valdinoci, Enrico 76 Vazquez, Juan Luis 60 Wei, Juncheng 58 Byun, Sun-Sig 56 Shahgholian, Henrik 56 Wang, Lihe 49 Figalli, Alessio 48 Lin, Chang-Shou 46 Sire, Yannick 45 Dipierro, Serena 45 Savin, Ovidiu V. 43 Zhang, Binlin 40 Quaas, Alexander 39 Ambrosio, Vincenzo 39 Li, YanYan 38 Lee, Ki-Ahm 38 Xiang, Mingqi 35 Friedman, Avner 33 Bao, Jiguang 33 Dong, Hongjie 33 Teixeira, Eduardo V. O. 33 Wang, Xu-Jia 32 Li, Dongsheng 32 Rădulescu, Vicenţiu D. 31 Farina, Alberto 31 Garofalo, Nicola 31 Trudinger, Neil Sidney 29 Ros-Oton, Xavier 28 Rossi, Julio Daniel 27 Kenig, Carlos Eduardo 27 Kim, Inwon Christina 27 Li, Congming 27 Novaga, Matteo 27 Petrosyan, Arshak 27 Squassina, Marco 26 Ferrari, Fausto 26 Kang, Dongsheng 26 Nyström, Kaj 26 Silvestre, Luis E. 25 Felmer, Patricio L. 25 Weiss, Georg Sebastian 24 Del Pino, Manuel A. 24 Musso, Monica 24 Peral Alonso, Ireneo 24 Terracini, Susanna 24 Vitolo, Antonio 23 De Silva, Daniela 23 Dolbeault, Jean 23 González, María del Mar 23 Gutiérrez, Cristian E. 23 Ivochkina, Nina Mikhaĭlovna 23 Nochetto, Ricardo Horacio 22 Chen, Wenxiong 22 Miyagaki, Olimpio Hiroshi 22 Seregin, Gregory A. 22 Sirakov, Boyan Slavchev 21 Hebey, Emmanuel 21 Niu, Pengcheng 21 Salsa, Sandro 21 Sciunzi, Berardino 21 Velichkov, Bozhidar 21 Wang, Kelei 21 Wolanski, Noemi I. 20 Abdellaoui, Boumediene 20 Bucur, Dorin 20 Karakhanyan, Aram L. 20 Lin, Fang Hua 20 Mingione, Giuseppe 20 Monneau, Régis 20 Serra Montolí, Joaquim 20 Stinga, Pablo Raúl 20 Yao, Fengping 20 Zhang, Lei 19 Bonforte, Matteo 19 Maldonado, Diego 19 McCann, Robert J. 19 Musina, Roberta 19 Salani, Paolo 19 Tang, Xianhua 18 Cabré, Xavier 18 Chen, Huyuan 18 da Silva, João Vítor 18 Dai, Limei 18 Krylov, Nicolaĭ Vladimirovich 18 Lu, Guozhen 18 Molica Bisci, Giovanni 18 Shivaji, Ratnasingham 18 Wang, Yanqing 18 Xiong, Jingang 18 Zou, Wenming 17 Chen, Caisheng 17 Chen, Zhen-Qing 17 De Philippis, Guido 17 Du, Lili 17 Fall, Mouhamed Moustapha 17 Guan, Pengfei 17 Gui, Changfeng 17 Liu, Jianguo 17 Ma, Xi-Nan ...and 5,545 more Authors
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#### Cited in 456 Serials

 518 Journal of Differential Equations 418 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 407 Calculus of Variations and Partial Differential Equations 309 Journal of Mathematical Analysis and Applications 262 Communications in Partial Differential Equations 258 Journal of Functional Analysis 236 Archive for Rational Mechanics and Analysis 191 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 188 Advances in Mathematics 169 Discrete and Continuous Dynamical Systems 159 Transactions of the American Mathematical Society 127 Proceedings of the American Mathematical Society 125 Journal de Mathématiques Pures et Appliquées. Neuvième Série 119 Communications on Pure and Applied Analysis 117 Communications in Mathematical Physics 103 Mathematische Annalen 89 SIAM Journal on Mathematical Analysis 87 Communications in Contemporary Mathematics 86 Annali di Matematica Pura ed Applicata. Serie Quarta 86 The Journal of Geometric Analysis 81 Communications on Pure and Applied Mathematics 75 Journal of Mathematical Sciences (New York) 70 Potential Analysis 68 NoDEA. Nonlinear Differential Equations and Applications 66 Journal of Mathematical Physics 61 Advanced Nonlinear Studies 57 Duke Mathematical Journal 56 Complex Variables and Elliptic Equations 55 Applied Mathematics Letters 54 Mathematische Zeitschrift 52 Computers & Mathematics with Applications 51 Manuscripta Mathematica 51 Nonlinear Analysis. Theory, Methods & Applications 48 Mathematical Methods in the Applied Sciences 48 Comptes Rendus. Mathématique. Académie des Sciences, Paris 45 Revista Matemática Iberoamericana 45 Journal of the European Mathematical Society (JEMS) 45 Advances in Nonlinear Analysis 44 Applicable Analysis 44 Journal of Mathematical Fluid Mechanics 43 Nonlinear Analysis. Real World Applications 42 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 42 Science China. Mathematics 41 Nonlinearity 39 Journal of Scientific Computing 39 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 37 Applied Mathematics and Optimization 36 ZAMP. Zeitschrift für angewandte Mathematik und Physik 36 Inventiones Mathematicae 36 Chinese Annals of Mathematics. Series B 35 Journal d’Analyse Mathématique 35 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 35 Boundary Value Problems 34 Acta Mathematica Sinica. English Series 31 Discrete and Continuous Dynamical Systems. Series B 30 Journal of Evolution Equations 29 Journal of Computational Physics 29 Acta Applicandae Mathematicae 27 Numerische Mathematik 27 Discrete and Continuous Dynamical Systems. Series S 27 Analysis & PDE 26 Journal of Computational and Applied Mathematics 26 Milan Journal of Mathematics 25 SIAM Journal on Numerical Analysis 24 Acta Mathematica 24 St. Petersburg Mathematical Journal 22 Journal für die Reine und Angewandte Mathematik 22 Journal of the American Mathematical Society 22 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 22 Abstract and Applied Analysis 22 Fractional Calculus & Applied Analysis 21 Mediterranean Journal of Mathematics 21 Advances in Calculus of Variations 20 Applied Mathematics and Computation 19 Israel Journal of Mathematics 19 Journal of Dynamics and Differential Equations 19 Interfaces and Free Boundaries 18 Topological Methods in Nonlinear Analysis 18 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 17 Rocky Mountain Journal of Mathematics 17 Bulletin of the American Mathematical Society. New Series 17 SIAM Journal on Scientific Computing 17 Electronic Journal of Differential Equations (EJDE) 16 International Journal of Mathematics 16 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 16 Journal of Fixed Point Theory and Applications 16 Kinetic and Related Models 15 Mathematics of Computation 15 Archiv der Mathematik 15 Memoirs of the American Mathematical Society 15 Probability Theory and Related Fields 15 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 15 Stochastic Processes and their Applications 15 Bulletin des Sciences Mathématiques 15 The Journal of Fourier Analysis and Applications 14 Bulletin of the Australian Mathematical Society 14 Arkiv för Matematik 14 Physica D 14 Acta Mathematicae Applicatae Sinica. English Series 14 Journal of Nonlinear Science ...and 356 more Serials
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#### Cited in 57 Fields

 6,592 Partial differential equations (35-XX) 996 Fluid mechanics (76-XX) 962 Calculus of variations and optimal control; optimization (49-XX) 567 Differential geometry (53-XX) 467 Global analysis, analysis on manifolds (58-XX) 421 Numerical analysis (65-XX) 417 Operator theory (47-XX) 337 Probability theory and stochastic processes (60-XX) 329 Real functions (26-XX) 324 Functional analysis (46-XX) 234 Potential theory (31-XX) 213 Integral equations (45-XX) 170 Harmonic analysis on Euclidean spaces (42-XX) 168 Mechanics of deformable solids (74-XX) 157 Statistical mechanics, structure of matter (82-XX) 123 Convex and discrete geometry (52-XX) 117 Ordinary differential equations (34-XX) 114 Quantum theory (81-XX) 112 Several complex variables and analytic spaces (32-XX) 111 Classical thermodynamics, heat transfer (80-XX) 98 Biology and other natural sciences (92-XX) 95 Measure and integration (28-XX) 86 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 85 Systems theory; control (93-XX) 80 Dynamical systems and ergodic theory (37-XX) 73 Geophysics (86-XX) 53 Operations research, mathematical programming (90-XX) 50 Optics, electromagnetic theory (78-XX) 48 Functions of a complex variable (30-XX) 26 Topological groups, Lie groups (22-XX) 25 Difference and functional equations (39-XX) 25 Mechanics of particles and systems (70-XX) 25 Relativity and gravitational theory (83-XX) 25 Astronomy and astrophysics (85-XX) 23 Abstract harmonic analysis (43-XX) 22 Approximations and expansions (41-XX) 21 Linear and multilinear algebra; matrix theory (15-XX) 19 Statistics (62-XX) 16 Computer science (68-XX) 14 Special functions (33-XX) 14 Geometry (51-XX) 13 Algebraic geometry (14-XX) 12 Information and communication theory, circuits (94-XX) 11 Integral transforms, operational calculus (44-XX) 10 General and overarching topics; collections (00-XX) 7 Combinatorics (05-XX) 6 History and biography (01-XX) 6 Number theory (11-XX) 6 General topology (54-XX) 6 Manifolds and cell complexes (57-XX) 4 Nonassociative rings and algebras (17-XX) 4 Algebraic topology (55-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 2 Group theory and generalizations (20-XX) 1 Mathematical logic and foundations (03-XX) 1 Sequences, series, summability (40-XX) 1 Mathematics education (97-XX)

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