Edit Profile (opens in new tab) Caffarelli, Luis Ángel Co-Author Distance Author ID: caffarelli.luis-a Published as: Caffarelli, Luis A.; Caffarelli, Luis; Caffarelli, L. A.; Caffarelli, L.; Caffarelli, Luis Ángel; Cafferelli, L. A. more...less Homepage: https://web.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) · Abel Prize (2023) Documents Indexed: 307 Publications since 1974, including 4 Books 7 Contributions as Editor · 2 Further Contributions Biographic References: 2 Publications Co-Authors: 132 Co-Authors with 257 Joint Publications 3,912 Co-Co-Authors all top 5 Co-Authors 58 single-authored 43 Friedman, Avner 18 Nirenberg, Louis 13 Athanasopoulos, Ioannis 13 Spruck, Joel 12 Alt, Hans Wilhelm 11 Salsa, Sandro 10 Silvestre, Luis E. 8 Mellet, Antoine 8 Vazquez, Juan Luis 7 Li, YanYan 6 Berestycki, Henri 6 Lin, Fang Hua 6 Markowich, Peter Alexander 6 Roquejoffre, Jean-Michel 6 Sire, Yannick 6 Vasseur, Alexis F. 5 Kenig, Carlos Eduardo 5 Lee, Ki-Ahm 5 Riviere, Nestor M. 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 Ambrosio, Luigi 3 Arapostathis, Aristotle 3 Burger, Martin 3 De Silva, Daniela 3 Huang, Qingbo 3 Jerison, David S. 3 Kohn, Robert Vita 3 Milakis, Emmanouil 3 Wolfram, Marie-Therese 2 Allen, Mark G. 2 Biswas, Anup 2 Bjorland, Clayton 2 Bonforte, Matteo 2 Brézis, Haïm 2 Calderón, Calixto Pedro 2 de la Llave, Rafael 2 Evans, Lawrence Craig 2 Fabes, Eugene B. 2 Gidas, Basilis 2 Grillo, Gabriele 2 Karakhanyan, Aram L. 2 Kinderlehrer, David 2 Kohn, Joseph J. 2 Lederman, Claudia B. 2 McCann, Robert J. 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 2 Yuan, Yu 1 Agmon, Shmuel 1 Birindelli, Isabeau 1 Brenier, Yann 1 Brezzi, Franco 1 Buttazzo, Giuseppe 1 Cagnetti, Filippo 1 Chan, Chi Hin 1 Chang, Kung-Ching 1 Chang, Sun-Yung Alice 1 Charro, Fernando 1 Dávila, Gonzalo 1 Guedes de Figueiredo, Djairo 1 Dipierro, Serena 1 Dolbeault, Jean 1 Dundas, Bjørn Ian 1 Duque, Luis 1 E, Weinan 1 Ekeland, Ivar 1 Fefferman, Charles Louis 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 Klainerman, Sergiu 1 Kocan, Maciej 1 Kochengin, Sergey A. 1 Kriventsov, Dennis ...and 50 more Co-Authors all top 5 Serials 36 Communications on Pure and Applied Mathematics 22 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 6 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 5 Discrete and Continuous Dynamical Systems 4 American Journal of Mathematics 4 Calculus of Variations and Partial Differential Equations 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 Notices of the American Mathematical Society 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 Analysis in Theory and Applications 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 1 Mathematics in Engineering 1 European Mathematical Society Magazine all top 5 Fields 263 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) 11 Operator theory (47-XX) 11 Global analysis, analysis on manifolds (58-XX) 11 Mechanics of deformable solids (74-XX) 11 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 History and biography (01-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Integral equations (45-XX) 6 Probability theory and stochastic processes (60-XX) 6 Statistical mechanics, structure of matter (82-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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 277 Publications have been cited 16,821 times in 9,714 Documents Cited by ▼ Year ▼ An extension problem related to the fractional Laplacian. Zbl 1143.26002Caffarelli, Luis; Silvestre, Luis 1,546 2007 Fully nonlinear elliptic equations. Zbl 0834.35002Caffarelli, Luis A.; Cabré, Xavier 688 1995 Partial regularity of suitable weak solutions of the Navier-Stokes equations. Zbl 0509.35067Caffarelli, L.; Kohn, R.; Nirenberg, Louis 669 1982 Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Zbl 0702.35085Caffarelli, Luis A.; Gidas, Basilis; Spruck, Joel 616 1989 First order interpolation inequalities with weights. Zbl 0563.46024Caffarelli, L.; Kohn, R.; Nirenberg, Louis 559 1984 Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063Caffarelli, Luis A.; Vasseur, Alexis 475 2010 The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian. Zbl 0654.35031Caffarelli, L.; Nirenberg, L.; Spruck, J. 423 1985 Existence and regularity for a minimum problem with free boundary. Zbl 0449.35105Alt, H. W.; Caffarelli, L. A. 349 1981 Interior a priori estimates for solutions of fully nonlinear equations. Zbl 0692.35017Caffarelli, Luis A. 322 1989 Regularity theory for fully nonlinear integro-differential equations. Zbl 1170.45006Caffarelli, Luis; Silvestre, Luis 315 2009 Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Zbl 1148.35097Caffarelli, Luis A.; Salsa, Sandro; Silvestre, Luis 293 2008 On \(W^{1,p}\) estimates for elliptic equations in divergence form. Zbl 0906.35030Caffarelli, L. A.; Peral, I. 291 1998 The Dirichlet problem for nonlinear second-order elliptic equations. I: Monge-Ampère equation. Zbl 0598.35047Caffarelli, L.; Nirenberg, Louis; Spruck, J. 283 1984 Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation. Zbl 0704.35044Caffarelli, Luis A. 243 1990 Nonlocal minimal surfaces. Zbl 1248.53009Caffarelli, L.; Roquejoffre, J.-M.; Savin, O. 224 2010 Non-local diffusions, drifts and games. Zbl 1266.35060Caffarelli, Luis 220 2012 Variational problems with two phases and their free boundary. Zbl 0844.35137Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 210 1984 The obstacle problem revisited. Zbl 0928.49030Caffarelli, L. A. 203 1998 A geometric approach to free boundary problems. Zbl 1083.35001Caffarelli, Luis; Salsa, Sandro 185 2005 On viscosity solutions of fully nonlinear equations with measurable ingredients. Zbl 0854.35032Caffarelli, L.; Crandall, M. G.; Kocan, M.; Świȩch, A. 174 1996 The regularity of free boundaries in higher dimensions. Zbl 0386.35046Caffarelli, Luis A. 167 1978 Boundary behavior of nonnegative solutions of elliptic operators in divergence form. Zbl 0512.35038Caffarelli, L.; Fabes, E.; Mortola, S.; Salsa, S. 164 1981 Variational problems with free boundaries for the fractional Laplacian. Zbl 1221.35453Caffarelli, Luis A.; Roquejoffre, Jean-Michel; Sire, Yannick 154 2010 A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity. Zbl 0704.35045Caffarelli, L. A. 151 1990 Further qualitative properties for elliptic equations in unbounded domains. Zbl 1079.35513Berestycki, Henri; Caffarelli, Luis; Nirenberg, Louis 149 1997 The Dirichlet problem for nonlinear second-order elliptic equations. II: Complex Monge-Ampère, and uniformly elliptic, equations. Zbl 0598.35048Caffarelli, L.; Kohn, J. J.; Nirenberg, Louis; Spruck, J. 147 1985 Monotonicity for elliptic equations in unbounded Lipschitz domains. Zbl 0906.35035Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 142 1997 The regularity of mappings with a convex potential. Zbl 0753.35031Caffarelli, Luis A. 140 1992 Regularity results for nonlocal equations by approximation. Zbl 1231.35284Caffarelli, Luis; Silvestre, Luis 126 2011 Vortex condensation in the Chern-Simons Higgs model: An existence theorem. Zbl 0846.58063Caffarelli, Luis A.; Yang, Yisong 123 1995 A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are \(C^{1,\alpha}\). Zbl 0676.35085Caffarelli, Luis A. 122 1987 Some regularity properties of solutions of Monge Ampère equation. Zbl 0761.35028Caffarelli, Luis A. 118 1991 A Harnack inequality approach to the regularity of free boundaries. II: Flat free boundaries are Lipschitz. Zbl 0676.35086Caffarelli, Luis A. 118 1989 Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105Caffarelli, Luis; Vazquez, Juan Luis 113 2011 Fractional elliptic equations, Caccioppoli estimates and regularity. Zbl 1381.35211Caffarelli, Luis A.; Stinga, Pablo Raúl 107 2016 Convexity of solutions of semilinear elliptic equations. Zbl 0599.35065Caffarelli, Luis A.; Friedman, Avner 102 1985 Boundary regularity of maps with convex potentials. II. Zbl 0916.35016Caffarelli, Luis A. 98 1996 Convexity properties of solutions to some classical variational problems. Zbl 0508.49013Caffarelli, Luis A.; Spruck, Joel 96 1982 Uniform estimates and limiting arguments for nonlocal minimal surfaces. Zbl 1357.49143Caffarelli, Luis; Valdinoci, Enrico 92 2011 A parabolic problem with a fractional time derivative. Zbl 1338.35428Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 92 2016 Inequalities for second-order elliptic equations with applications to unbounded domains. I. Zbl 0860.35004Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 90 1996 Properties of the solutions of the linearized Monge-Ampère equation. Zbl 0878.35039Caffarelli, Luis A.; Gutiérrez, Cristian E. 88 1997 The initial trace of a solution of the porous medium equation. Zbl 0556.76084Aronson, D. G.; Caffarelli, L. A. 88 1983 Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis 86 2011 Boundary regularity of maps with convex potentials. Zbl 0778.35015Caffarelli, Luis A. 80 1992 The Evans-Krylov theorem for nonlocal fully nonlinear equations. Zbl 1232.49043Caffarelli, Luis; Silvestre, Luis 79 2011 Regularity of the free boundary of a gas flow in an \(n\)-dimensional porous medium. Zbl 0439.76085Caffarelli, Luis A.; Friedman, Avner 77 1980 A Harnack inequality approach to the regularity of free boundaries. III: Existence theory, compactness, and dependence on X. Zbl 0702.35249Caffarelli, Luis A. 76 1988 Nonlinear second-order elliptic equations. V: The Dirichlet problem for Weingarten hypersurfaces. Zbl 0672.35028Caffarelli, Luis; Nirenberg, Louis; Spruck, Joel 76 1988 Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. Zbl 1194.35138Caffarelli, L. A.; Lin, Fang-Hua 74 2008 An extension to a theorem of Jörgens, Calabi, and Pogorelov. Zbl 1236.35041Caffarelli, L.; Li, YanYan 73 2003 Monotonicity properties of optimal transportation and the FKG and related inequalities. Zbl 0978.60107Caffarelli, Luis A. 72 2000 Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs. Zbl 1053.49032Caffarelli, Luis A.; Feldman, Mikhail; McCann, Robert J. 72 2002 Further regularity for the Signorini problem. Zbl 0427.35019Caffarelli, L. A. 71 1979 Regularity of a free boundary with application to the Pompeiu problem. Zbl 0960.35112Caffarelli, Luis A.; Karp, Lavi; Shahgholian, Henrik 71 2000 Continuity of the temperature in the two-phase Stefan problem. Zbl 0516.35080Caffarelli, L. A.; Evans, L. C. 70 1983 The structure of the free boundary for lower dimensional obstacle problems. Zbl 1185.35339Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. 69 2008 An \(L^ \infty\) bound for solutions of the Cahn-Hilliard equation. Zbl 0851.35010Caffarelli, Luis A.; Muler, Nora E. 67 1995 Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media. Zbl 1063.35025Caffarelli, Luis A.; Souganidis, Panagiotis E.; Wang, L. 66 2005 Some new monotonicity theorems with applications to free boundary problems. Zbl 1142.35382Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E. 62 2002 Global energy minimizers for free boundary problems and full regularity in three dimensions. Zbl 1330.35545Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E. 62 2004 A free boundary problem for quasi-linear elliptic equations. Zbl 0554.35129Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 62 1984 Non-local gradient dependent operators. Zbl 1252.35099Bjorland, C.; Caffarelli, L.; Figalli, A. 62 2012 Lipschitz continuity of solutions and interfaces of the N-dimensional porous medium equation. Zbl 0644.35058Caffarelli, L. A.; Vazquez, J. L.; Wolanski, N. I. 60 1987 Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088Caffarelli, Luis; Figalli, Alessio 60 2013 The obstacle problem for the biharmonic operator. Zbl 0405.31007Caffarelli, Luis A.; Friedman, Avner 59 1979 Uniform estimates for regularization of free boundary problems. Zbl 0702.35252Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 59 1990 Uniform convergence of a singular perturbation problem. Zbl 0829.49013Caffarelli, Luis A.; Córdoba, Antonio 59 1995 Completely singular elliptic-harmonic measures. Zbl 0482.35020Caffarelli, Luis A.; Fabes, Eugene B.; Kenig, Carlos E. 58 1981 A free-boundary problem for the heat equation arising in flame propagation. Zbl 0814.35149Caffarelli, Luis A.; Vázquez, Juan L. 56 1995 An optimal partition problem for eigenvalues. Zbl 1123.65060Cafferelli, L. A.; Lin, Fang Hua 56 2007 Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio 56 2012 Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations. Zbl 0593.35047Caffarelli, Luis A.; Friedman, Avner 56 1985 Optimal transportation and applications. Lectures given at the C. I. M. E. summer school, Martina Franca, Italy, September 2–8, 2001. Zbl 1013.00028Ambrosio, Luigi; Brenier, Yann; Buttazzo, Giusseppe; Caffarelli, Luis A.; Villani, Cédric 55 2003 Optimal regularity of lower dimensional obstacle problems. Zbl 1108.35038Athanasopoulos, I.; Caffarelli, L. A. 54 2004 Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis 54 2013 Regularity properties of nonlocal minimal surfaces via limiting arguments. Zbl 1284.53008Caffarelli, Luis; Valdinoci, Enrico 54 2013 Compactness methods in free boundary problems. Zbl 0437.35070Caffarelli, Luis A. 52 1980 Free boundaries in optimal transport and Monge-Ampère obstacle problems. Zbl 1196.35231Caffarelli, Luis A.; McCann, Robert J. 52 2010 A gradient bound for entire solutions of quasi-linear equations and its consequences. Zbl 0819.35016Caffarelli, Luis; Garofalo, Nicola; Segala, Fausto 52 1994 Rates of convergence for the homogenization of fully nonlinear uniformly elliptic PDE in random media. Zbl 1192.35048Caffarelli, Luis A.; Souganidis, Panagiotis E. 50 2010 Potential methods in variational inequalities. Zbl 0455.49010Caffarelli, L. A.; Kinderlehrer, D. 49 1980 Nonlinear second order elliptic equations. IV. Starshaped compact Weingarten hypersurfaces. Zbl 0672.35027Caffarelli, L.; Nirenberg, L.; Spruck, J. 49 1986 Continuity of the density of a gas flow in a porous medium. Zbl 0425.35060Caffarelli, Luis A.; Friedman, Avner 48 1979 Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043Caffarelli, Luis; Vázquez, Juan-Luis 46 2011 Symmetry for elliptic equations in a half space. Zbl 0793.35034Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 46 1993 Real analysis related to the Monge-Ampère equation. Zbl 0858.35034Caffarelli, Luis A.; Gutiérrez, Cristian E. 45 1996 Regularity of a free boundary in parabolic potential theory. Zbl 1054.35142Caffarelli, Luis; Petrosyan, Arshak; Shahgholian, Henrik 45 2004 On the case of equality in the Brunn-Minkowski inequality for capacity. Zbl 0847.31005Caffarelli, Luis A.; Jerison, David; Lieb, Elliott H. 44 1996 Planelike minimizers in periodic media. Zbl 1036.49040Caffarelli, Luis A.; de la Llave, Rafael 44 2001 Some remarks on singular solutions of nonlinear elliptic equations. III: Viscosity solutions including parabolic operators. Zbl 1279.35044Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis 44 2013 The blow-up boundary for nonlinear wave equations. Zbl 0638.35053Caffarelli, Luis A.; Friedman, Avner 44 1986 An optimization problem with volume constraint. Zbl 0588.49005Aguilera, N.; Alt, H. W.; Caffarelli, L. A. 44 1986 The shape of axisymmetric rotating fluid. Zbl 0439.35068Caffarelli, Luis A.; Friedman, Avner 43 1980 Asymptotic estimates for the plasma problem. Zbl 0466.35033Caffarelli, Luis A.; Friedman, Avner 43 1980 Regularity of the free boundary in parabolic phase-transition problems. Zbl 0891.35164Athanasopoulos, I.; Caffarelli, L.; Salsa, S. 42 1996 Reinforcement problems for elliptic equations and variational inequalities. Zbl 0434.35079Brézis, Haïm; Caffarelli, Luis A.; Friedman, Avner 41 1980 Convergence of nonlocal threshold dynamics approximations to front propagation. Zbl 1190.65132Caffarelli, Luis A.; Souganidis, Panagiotis E. 41 2010 Continuity of the temperature in boundary heat control problems. Zbl 1190.35125Athanasopoulos, I.; Caffarelli, L. A. 41 2010 Allocation maps with general cost functions. Zbl 0883.49030Caffarelli, Luis A. 40 1996 Regularity for \(C^{1, \alpha}\) interface transmission problems. Zbl 1467.35169Caffarelli, Luis Ángel; Soria-Carro, María; Stinga, Pablo Raúl 7 2021 The leading edge of a free boundary interacting with a line of fast diffusion. Zbl 1465.35414Caffarelli, L. A.; Roquejoffre, J.-M. 1 2021 Fully nonlinear integro-differential equations with deforming kernels. Zbl 1452.35055Caffarelli, Luis; Teymurazyan, Rafayel; Urbano, José Miguel 5 2020 Existence of weak solutions to a continuity equation with space time nonlocal Darcy law. Zbl 1459.35233Caffarelli, Luis; Gualdani, Maria; Zamponi, Nicola 4 2020 Optimal regularity and structure of the free boundary for minimizers in cohesive zone models. Zbl 1442.49005Caffarelli, L.; Cagnetti, F.; Figalli, A. 2 2020 Minimal surfaces and free boundaries: recent developments. Zbl 1433.35464Caffarelli, Luis A.; Sire, Yannick 1 2020 Ergodic control of a class of jump diffusions with finite Lévy measures and rough kernels. Zbl 1415.93288Arapostathis, Ari; Caffarelli, Luis; Pang, Guodong; Zheng, Yi 7 2019 Parabolic obstacle problems, quasi-convexity and regularity. Zbl 1432.35264Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil 6 2019 Interior regularity for fractional systems. Zbl 1411.35111Caffarelli, Luis; Dávila, Gonzalo 5 2019 On uniqueness of solutions to viscous HJB equations with a subquadratic nonlinearity in the gradient. Zbl 1428.35125Arapostathis, Ari; Biswas, Anup; Caffarelli, Luis 4 2019 Regularity of interfaces for a Pucci type segregation problem. Zbl 1432.35085Caffarelli, L.; Patrizi, S.; Quitalo, V.; Torres, M. 1 2019 On the regularity of the non-dynamic parabolic fractional obstacle problem. Zbl 1394.35588Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil 19 2018 A minimization problem with free boundary related to a cooperative system. Zbl 1395.35226Caffarelli, Luis A.; Shahgholian, Henrik; Yeressian, Karen 16 2018 Two-phase anisotropic free boundary problems and applications to the Bellman equation in 2D. Zbl 1393.35247Caffarelli, L.; De Silva, D.; Savin, O. 6 2018 Bounds on the Green function for integral operators and fractional harmonic measure with applications to boundary Harnack. Zbl 1387.35071Caffarelli, Luis A.; Sire, Yannick 3 2018 Obstacle problems for integro-differential operators: regularity of solutions and free boundaries. Zbl 1371.35361Caffarelli, Luis; Ros-Oton, Xavier; Serra, Joaquim 40 2017 Porous medium flow with both a fractional potential pressure and fractional time derivative. Zbl 1372.35328Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 24 2017 A logistic equation with nonlocal interactions. Zbl 1356.35261Caffarelli, Luis; Dipierro, Serena; Valdinoci, Enrico 21 2017 On some pointwise inequalities involving nonlocal operators. Zbl 1482.35017Caffarelli, Luis A.; Sire, Yannick 16 2017 The two membranes problem for different operators. Zbl 1368.35045Caffarelli, L.; De Silva, D.; Savin, O. 15 2017 On a long range segregation model. Zbl 1386.35084Caffarelli, L.; Patrizi, S.; Quitalo, V. 7 2017 Fractional elliptic equations, Caccioppoli estimates and regularity. Zbl 1381.35211Caffarelli, Luis A.; Stinga, Pablo Raúl 107 2016 A parabolic problem with a fractional time derivative. Zbl 1338.35428Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 92 2016 A free boundary problem related to thermal insulation. Zbl 1351.35268Caffarelli, Luis A.; Kriventsov, Dennis 17 2016 The Dirichlet problem for stable-like operators and related probabilistic representations. Zbl 1352.60080Arapostathis, Ari; Biswas, Anup; Caffarelli, Luis 15 2016 Obstacle-type problems for minimal surfaces. Zbl 1370.35070Caffarelli, L.; De Silva, D.; Savin, O. 13 2016 Regularity of solutions of the fractional porous medium flow with exponent \(1/2\). Zbl 1335.35273Caffarelli, L.; Vázquez, J. L. 13 2016 A non-local Monge-Ampère equation. Zbl 1361.35067Caffarelli, Luis; Silvestre, Luis 5 2016 Minimization of a fractional perimeter-Dirichlet integral functional. Zbl 1323.35216Caffarelli, Luis; Savin, Ovidiu; Valdinoci, Enrico 14 2015 On a fractional Monge-Ampère operator. Zbl 1393.35268Caffarelli, Luis; Charro, Fernando 11 2015 Regularity of free boundaries a heuristic retro. Zbl 1353.35319Caffarelli, Luis A.; Shahgholian, Henrik 4 2015 A bifurcation phenomenon in a singularly perturbed one-phase free boundary problem of phase transition. Zbl 1334.35439Caffarelli, Luis A.; Wang, Peiyong 3 2015 Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities. Zbl 1296.35208Caffarelli, Luis; Jin, Tianling; Sire, Yannick; Xiong, Jingang 38 2014 Partial differential equation models in the socio-economic sciences. Zbl 1353.00004 15 2014 Hölder regularity for generalized master equations with rough kernels. Zbl 1312.45013Caffarelli, Luis; Silvestre, Luis 13 2014 On the asymptotic behavior of a Boltzmann-type price formation model. Zbl 1307.35302Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 9 2014 Regularity for anisotropic fully nonlinear integro-differential equations. Zbl 1304.35730Caffarelli, Luis A.; Leitão, Raimundo; Urbano, José Miguel 7 2014 A perturbation argument for a Monge-Ampère type equation arising in optimal transportation. Zbl 1294.35170Caffarelli, Luis; Del Mar González, María; Nguyen, Truyen 6 2014 Counter-example in three dimension and homogenization of geometric motions in two dimension. Zbl 1293.35026Caffarelli, L. A.; Monneau, R. 5 2014 Relations between geometric convexity, doubling measures and property \(\Gamma\). Zbl 1307.46006Caffarelli, Luis A.; Crandall, Michael G. 2 2014 Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088Caffarelli, Luis; Figalli, Alessio 60 2013 Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis 54 2013 Regularity properties of nonlocal minimal surfaces via limiting arguments. Zbl 1284.53008Caffarelli, Luis; Valdinoci, Enrico 54 2013 Some remarks on singular solutions of nonlinear elliptic equations. III: Viscosity solutions including parabolic operators. Zbl 1279.35044Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis 44 2013 On a Boltzmann-type price formation model. Zbl 1372.91039Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 18 2013 A priori bounds for solutions of a nonlocal evolution PDE. Zbl 1273.35067Caffarelli, Luis; Valdinoci, Enrico 8 2013 The homogenization of surfaces and boundaries. Zbl 1296.35030Caffarelli, Luis 1 2013 Non-local diffusions, drifts and games. Zbl 1266.35060Caffarelli, Luis 220 2012 Non-local gradient dependent operators. Zbl 1252.35099Bjorland, C.; Caffarelli, L.; Figalli, A. 62 2012 Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio 56 2012 Some remarks on singular solutions of nonlinear elliptic equations. II: Symmetry and monotonicity via moving planes. Zbl 1325.35044Caffarelli, Luis; Li, YanYan; Nirenberg, Louis 20 2012 Traveling waves for a boundary reaction-diffusion equation. Zbl 1255.35072Caffarelli, L.; Mellet, A.; Sire, Y. 10 2012 The De Giorgi method for nonlocal fluid dynamics. Zbl 1357.35249Caffarelli, Luis A.; Vasseur, Alexis 6 2012 The problem of two sticks. Zbl 1257.46009Caffarelli, Luis A.; Crandall, Michael G. 1 2012 Regularity results for nonlocal equations by approximation. Zbl 1231.35284Caffarelli, Luis; Silvestre, Luis 126 2011 Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105Caffarelli, Luis; Vazquez, Juan Luis 113 2011 Uniform estimates and limiting arguments for nonlocal minimal surfaces. Zbl 1357.49143Caffarelli, Luis; Valdinoci, Enrico 92 2011 Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis 86 2011 The Evans-Krylov theorem for nonlocal fully nonlinear equations. Zbl 1232.49043Caffarelli, Luis; Silvestre, Luis 79 2011 Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043Caffarelli, Luis; Vázquez, Juan-Luis 46 2011 On a price formation free boundary model by Lasry and Lions. Zbl 1216.91012Caffarelli, Luis A.; Markowich, Peter A.; Pietschmann, Jan-F. 14 2011 On a price formation free boundary model by Lasry and Lions: the Neumann problem. Zbl 1233.91336Caffarelli, Luis A.; Markowich, Peter A.; Wolfram, Marie-Therese 8 2011 Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063Caffarelli, Luis A.; Vasseur, Alexis 475 2010 Nonlocal minimal surfaces. Zbl 1248.53009Caffarelli, L.; Roquejoffre, J.-M.; Savin, O. 224 2010 Variational problems with free boundaries for the fractional Laplacian. Zbl 1221.35453Caffarelli, Luis A.; Roquejoffre, Jean-Michel; Sire, Yannick 154 2010 Free boundaries in optimal transport and Monge-Ampère obstacle problems. Zbl 1196.35231Caffarelli, Luis A.; McCann, Robert J. 52 2010 Rates of convergence for the homogenization of fully nonlinear uniformly elliptic PDE in random media. Zbl 1192.35048Caffarelli, Luis A.; Souganidis, Panagiotis E. 50 2010 Convergence of nonlocal threshold dynamics approximations to front propagation. Zbl 1190.65132Caffarelli, Luis A.; Souganidis, Panagiotis E. 41 2010 Continuity of the temperature in boundary heat control problems. Zbl 1190.35125Athanasopoulos, I.; Caffarelli, L. A. 41 2010 Distance functions and almost global solutions of eikonal equations. Zbl 1187.35024Caffarelli, Luis A.; Crandall, Michael G. 17 2010 The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Zbl 1210.76039Caffarelli, Luis A.; Vasseur, Alexis F. 17 2010 Analysis on the junctions of domain walls. Zbl 1193.35255Caffarelli, Luis A.; Lin, Fang Hua 9 2010 On the Evans-Krylov theorem. Zbl 1180.35229Caffarelli, Luis; Silvestre, Luis 8 2010 Smooth approximations of solutions to nonconvex fully nonlinear elliptic equations. Zbl 1208.35047Caffarelli, Luis; Silvestre, Luis 7 2010 Regularity theory for fully nonlinear integro-differential equations. Zbl 1170.45006Caffarelli, Luis; Silvestre, Luis 315 2009 Some remarks on singular solutions of nonlinear elliptic equations. I. Zbl 1215.35068Caffarelli, Luis; Li, Yan Yan; Nirenberg, Louis 38 2009 The geometry of solutions to a segregation problem for nondivergence systems. Zbl 1217.35015Caffarelli, L. A.; Karakhanyan, A. L.; Lin, Fang-Hua 27 2009 Random homogenization of an obstacle problem. Zbl 1180.35069Caffarelli, L. A.; Mellet, A. 19 2009 Nonlocal heat flows preserving the \(L^2\) energy. Zbl 1154.35364Caffarelli, Luis; Lin, Fanghua 19 2009 Surfaces minimizing nonlocal energies. Zbl 1182.53055Caffarelli, Luis A. 12 2009 Reflector problem in \({\mathbb R^n}\) endowed with non-Euclidean norm. Zbl 1173.78003Caffarelli, Luis A.; Huang, Qingbo 6 2009 Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Zbl 1148.35097Caffarelli, Luis A.; Salsa, Sandro; Silvestre, Luis 293 2008 Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. Zbl 1194.35138Caffarelli, L. A.; Lin, Fang-Hua 74 2008 The structure of the free boundary for lower dimensional obstacle problems. Zbl 1185.35339Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. 69 2008 A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs. Zbl 1140.65075Caffarelli, Luis A.; Souganidis, Panagiotis E. 36 2008 Weak solutions of one inverse problem in geometric optics. Zbl 1202.78003Caffarelli, L. A.; Oliker, V. I. 26 2008 On the regularity of reflector antennas. Zbl 1140.35009Caffarelli, Luis A.; Gutiíerrez, Cristian E.; Huang, Qingbo 23 2008 Random homogenization of fractional obstacle problems. Zbl 1156.74359Caffarelli, Luis; Mellet, Antoine 12 2008 A counterexample to \(C^{2,1}\) regularity for parabolic fully nonlinear equations. Zbl 1162.35042Caffarelli, Luis A.; Stefanelli, Ulisse 10 2008 Some nonlinear problems involving nonlocal diffusions. Zbl 1419.35203Caffarelli, Luis A. 8 2008 Numerical solution of the Dirichlet problem for a Pucci equation in dimension two. Application to homogenization. Zbl 1155.65097Caffarelli, L. A.; Glowinski, R. 6 2008 Viscosity method for homogenization of highly oscillating obstacles. Zbl 1158.35109Caffarelli, Luis; Lee, Ki-Ahm 6 2008 An extension problem related to the fractional Laplacian. Zbl 1143.26002Caffarelli, Luis; Silvestre, Luis 1,546 2007 An optimal partition problem for eigenvalues. Zbl 1123.65060Cafferelli, L. A.; Lin, Fang Hua 56 2007 A constant rank theorem for solutions of fully nonlinear elliptic equations. Zbl 1191.35127Caffarelli, Luis A.; Guan, Pengfei; Ma, Xinan 33 2007 Uniform Hölder estimates in a class of elliptic systems and applications to singular limits in models for diffusion flames. Zbl 1189.35084Caffarelli, Luis A.; Roquejoffre, Jean-Michel 19 2007 Capillary drops: contact angle hysteresis and sticking drops. Zbl 1168.76007Caffarelli, L. A.; Mellet, A. 17 2007 Capillary drops on an inhomogeneous surface. Zbl 1200.76053Caffarelli, L. A.; Mellet, A. 11 2007 Homogenization of oscillating free boundaries: the elliptic case. Zbl 1122.35156Caffarelli, L.; Lee, K. 6 2007 Flame propagation in one-dimensional stationary ergodic media. Zbl 1110.76054Caffarelli, L. A.; Lee, K.-A.; Mellet, A. 4 2007 ...and 177 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 6,848 Authors 129 Caffarelli, Luis Ángel 122 Valdinoci, Enrico 78 Vazquez, Juan Luis 70 Byun, Sun-Sig 69 Wei, Juncheng 67 Shahgholian, Henrik 62 Dipierro, Serena 57 Wang, Lihe 53 Savin, Ovidiu V. 52 Figalli, Alessio 52 Sire, Yannick 51 Zhang, Binlin 48 Lin, Chang-Shou 45 Xiang, Mingqi 44 Lee, Ki-Ahm 44 Quaas, Alexander 43 Garofalo, Nicola 42 Ambrosio, Vincenzo 42 Bao, Jiguang 41 Dong, Hongjie 39 Li, YanYan 39 Rădulescu, Vicenţiu D. 37 Teixeira, Eduardo V. 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