Edit Profile (opens in new tab) Caffarelli, Luis Ángel Compute Distance To: Compute 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: 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: 305 Publications since 1974, including 4 Books 7 Contributions as Editor · 1 Further Contribution Biographic References: 1 Publication Co-Authors: 128 Co-Authors with 253 Joint Publications 3,699 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 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 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 1 Lax, Peter David 1 Leitão, Raimundo A. 1 Lieb, Elliott Hershel ...and 44 more Co-Authors all top 5 Serials 35 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 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 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 all top 5 Fields 261 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 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) 5 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 272 Publications have been cited 14,933 times in 8,710 Documents Cited by ▼ Year ▼ An extension problem related to the fractional Laplacian. Zbl 1143.26002Caffarelli, Luis; Silvestre, Luis 1,361 2007 Partial regularity of suitable weak solutions of the Navier-Stokes equations. Zbl 0509.35067Caffarelli, L.; Kohn, R.; Nirenberg, Louis 617 1982 Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Zbl 0702.35085Caffarelli, Luis A.; Gidas, Basilis; Spruck, Joel 547 1989 Fully nonlinear elliptic equations. Zbl 0834.35002Caffarelli, Luis A.; Cabré, Xavier 526 1995 First order interpolation inequalities with weights. Zbl 0563.46024Caffarelli, L.; Kohn, R.; Nirenberg, Louis 510 1984 Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063Caffarelli, Luis A.; Vasseur, Alexis 411 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. 367 1985 Existence and regularity for a minimum problem with free boundary. Zbl 0449.35105Alt, H. W.; Caffarelli, L. A. 313 1981 Interior a priori estimates for solutions of fully nonlinear equations. Zbl 0692.35017Caffarelli, Luis A. 288 1989 On \(W^{1,p}\) estimates for elliptic equations in divergence form. Zbl 0906.35030Caffarelli, L. A.; Peral, I. 270 1998 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 267 2008 Regularity theory for fully nonlinear integro-differential equations. Zbl 1170.45006Caffarelli, Luis; Silvestre, Luis 267 2009 The Dirichlet problem for nonlinear second-order elliptic equations. I: Monge-Ampère equation. Zbl 0598.35047Caffarelli, L.; Nirenberg, Louis; Spruck, J. 256 1984 Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation. Zbl 0704.35044Caffarelli, Luis A. 200 1990 Nonlocal minimal surfaces. Zbl 1248.53009Caffarelli, L.; Roquejoffre, J.-M.; Savin, O. 198 2010 Non-local diffusions, drifts and games. Zbl 1266.35060Caffarelli, Luis 189 2012 Variational problems with two phases and their free boundary. Zbl 0844.35137Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 182 1984 The obstacle problem revisited. Zbl 0928.49030Caffarelli, L. A. 179 1998 A geometric approach to free boundary problems. Zbl 1083.35001Caffarelli, Luis; Salsa, Sandro 157 2005 The regularity of free boundaries in higher dimensions. Zbl 0386.35046Caffarelli, Luis A. 156 1978 On viscosity solutions of fully nonlinear equations with measurable ingredients. Zbl 0854.35032Caffarelli, L.; Crandall, M. G.; Kocan, M.; Świȩch, A. 155 1996 Boundary behavior of nonnegative solutions of elliptic operators in divergence form. Zbl 0512.35038Caffarelli, L.; Fabes, E.; Mortola, S.; Salsa, S. 153 1981 Further qualitative properties for elliptic equations in unbounded domains. Zbl 1079.35513Berestycki, Henri; Caffarelli, Luis; Nirenberg, Louis 136 1997 Variational problems with free boundaries for the fractional Laplacian. Zbl 1221.35453Caffarelli, Luis A.; Roquejoffre, Jean-Michel; Sire, Yannick 135 2010 A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity. Zbl 0704.35045Caffarelli, L. A. 131 1990 Monotonicity for elliptic equations in unbounded Lipschitz domains. Zbl 0906.35035Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 128 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. 125 1985 The regularity of mappings with a convex potential. Zbl 0753.35031Caffarelli, Luis A. 118 1992 Regularity results for nonlocal equations by approximation. Zbl 1231.35284Caffarelli, Luis; Silvestre, Luis 113 2011 Vortex condensation in the Chern-Simons Higgs model: An existence theorem. Zbl 0846.58063Caffarelli, Luis A.; Yang, Yisong 112 1995 Some regularity properties of solutions of Monge Ampère equation. Zbl 0761.35028Caffarelli, Luis A. 108 1991 A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are \(C^{1,\alpha}\). Zbl 0676.35085Caffarelli, Luis A. 104 1987 A Harnack inequality approach to the regularity of free boundaries. II: Flat free boundaries are Lipschitz. Zbl 0676.35086Caffarelli, Luis A. 104 1989 Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105Caffarelli, Luis; Vazquez, Juan Luis 98 2011 Convexity of solutions of semilinear elliptic equations. Zbl 0599.35065Caffarelli, Luis A.; Friedman, Avner 96 1985 Convexity properties of solutions to some classical variational problems. Zbl 0508.49013Caffarelli, Luis A.; Spruck, Joel 92 1982 Fractional elliptic equations, Caccioppoli estimates and regularity. Zbl 1381.35211Caffarelli, Luis A.; Stinga, Pablo Raúl 90 2016 Boundary regularity of maps with convex potentials. II. Zbl 0916.35016Caffarelli, Luis A. 86 1996 Inequalities for second-order elliptic equations with applications to unbounded domains. I. Zbl 0860.35004Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 86 1996 The initial trace of a solution of the porous medium equation. Zbl 0556.76084Aronson, D. G.; Caffarelli, L. A. 84 1983 Uniform estimates and limiting arguments for nonlocal minimal surfaces. Zbl 1357.49143Caffarelli, Luis; Valdinoci, Enrico 82 2011 A parabolic problem with a fractional time derivative. Zbl 1338.35428Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 81 2016 Properties of the solutions of the linearized Monge-Ampère equation. Zbl 0878.35039Caffarelli, Luis A.; Gutiérrez, Cristian E. 81 1997 Boundary regularity of maps with convex potentials. Zbl 0778.35015Caffarelli, Luis A. 73 1992 Regularity of the free boundary of a gas flow in an \(n\)-dimensional porous medium. Zbl 0439.76085Caffarelli, Luis A.; Friedman, Avner 73 1980 Nonlinear second-order elliptic equations. V: The Dirichlet problem for Weingarten hypersurfaces. Zbl 0672.35028Caffarelli, Luis; Nirenberg, Louis; Spruck, Joel 72 1988 The Evans-Krylov theorem for nonlocal fully nonlinear equations. Zbl 1232.49043Caffarelli, Luis; Silvestre, Luis 72 2011 Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis 71 2011 Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. Zbl 1194.35138Caffarelli, L. A.; Lin, Fang-Hua 67 2008 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. 66 2002 Continuity of the temperature in the two-phase Stefan problem. Zbl 0516.35080Caffarelli, L. A.; Evans, L. C. 66 1983 A Harnack inequality approach to the regularity of free boundaries. III: Existence theory, compactness, and dependence on X. Zbl 0702.35249Caffarelli, Luis A. 66 1988 Further regularity for the Signorini problem. Zbl 0427.35019Caffarelli, L. A. 65 1979 Regularity of a free boundary with application to the Pompeiu problem. Zbl 0960.35112Caffarelli, Luis A.; Karp, Lavi; Shahgholian, Henrik 62 2000 An extension to a theorem of Jörgens, Calabi, and Pogorelov. Zbl 1236.35041Caffarelli, L.; Li, YanYan 61 2003 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. 61 2005 Monotonicity properties of optimal transportation and the FKG and related inequalities. Zbl 0978.60107Caffarelli, Luis A. 58 2000 The structure of the free boundary for lower dimensional obstacle problems. Zbl 1185.35339Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. 58 2008 Lipschitz continuity of solutions and interfaces of the N-dimensional porous medium equation. Zbl 0644.35058Caffarelli, L. A.; Vazquez, J. L.; Wolanski, N. I. 57 1987 An \(L^ \infty\) bound for solutions of the Cahn-Hilliard equation. Zbl 0851.35010Caffarelli, Luis A.; Muler, Nora E. 57 1995 Uniform estimates for regularization of free boundary problems. Zbl 0702.35252Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 56 1990 Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations. Zbl 0593.35047Caffarelli, Luis A.; Friedman, Avner 55 1985 An optimal partition problem for eigenvalues. Zbl 1123.65060Cafferelli, L. A.; Lin, Fang Hua 54 2007 Some new monotonicity theorems with applications to free boundary problems. Zbl 1142.35382Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E. 54 2002 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 54 2003 A free boundary problem for quasi-linear elliptic equations. Zbl 0554.35129Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 54 1984 Non-local gradient dependent operators. Zbl 1252.35099Bjorland, C.; Caffarelli, L.; Figalli, A. 54 2012 Global energy minimizers for free boundary problems and full regularity in three dimensions. Zbl 1330.35545Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E. 53 2004 Uniform convergence of a singular perturbation problem. Zbl 0829.49013Caffarelli, Luis A.; Córdoba, Antonio 53 1995 The obstacle problem for the biharmonic operator. Zbl 0405.31007Caffarelli, Luis A.; Friedman, Avner 53 1979 Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio 53 2012 Completely singular elliptic-harmonic measures. Zbl 0482.35020Caffarelli, Luis A.; Fabes, Eugene B.; Kenig, Carlos E. 51 1981 Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088Caffarelli, Luis; Figalli, Alessio 51 2013 A free-boundary problem for the heat equation arising in flame propagation. Zbl 0814.35149Caffarelli, Luis A.; Vázquez, Juan L. 50 1995 A gradient bound for entire solutions of quasi-linear equations and its consequences. Zbl 0819.35016Caffarelli, Luis; Garofalo, Nicola; Segala, Fausto 50 1994 Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis 49 2013 Compactness methods in free boundary problems. Zbl 0437.35070Caffarelli, Luis A. 48 1980 Regularity properties of nonlocal minimal surfaces via limiting arguments. Zbl 1284.53008Caffarelli, Luis; Valdinoci, Enrico 48 2013 Optimal regularity of lower dimensional obstacle problems. Zbl 1108.35038Athanasopoulos, I.; Caffarelli, L. A. 46 2004 Free boundaries in optimal transport and Monge-Ampère obstacle problems. Zbl 1196.35231Caffarelli, Luis A.; McCann, Robert J. 46 2010 Continuity of the density of a gas flow in a porous medium. Zbl 0425.35060Caffarelli, Luis A.; Friedman, Avner 45 1979 Potential methods in variational inequalities. Zbl 0455.49010Caffarelli, L. A.; Kinderlehrer, D. 45 1980 Rates of convergence for the homogenization of fully nonlinear uniformly elliptic PDE in random media. Zbl 1192.35048Caffarelli, Luis A.; Souganidis, Panagiotis E. 44 2010 Regularity of a free boundary in parabolic potential theory. Zbl 1054.35142Caffarelli, Luis; Petrosyan, Arshak; Shahgholian, Henrik 43 2004 Real analysis related to the Monge-Ampère equation. Zbl 0858.35034Caffarelli, Luis A.; Gutiérrez, Cristian E. 43 1996 Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043Caffarelli, Luis; Vázquez, Juan-Luis 43 2011 Nonlinear second order elliptic equations. IV. Starshaped compact Weingarten hypersurfaces. Zbl 0672.35027Caffarelli, L.; Nirenberg, L.; Spruck, J. 43 1986 Symmetry for elliptic equations in a half space. Zbl 0793.35034Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 42 1993 Planelike minimizers in periodic media. Zbl 1036.49040Caffarelli, Luis A.; de la Llave, Rafael 42 2001 The blow-up boundary for nonlinear wave equations. Zbl 0638.35053Caffarelli, Luis A.; Friedman, Avner 42 1986 An optimization problem with volume constraint. Zbl 0588.49005Aguilera, N.; Alt, H. W.; Caffarelli, L. A. 42 1986 On the case of equality in the Brunn-Minkowski inequality for capacity. Zbl 0847.31005Caffarelli, Luis A.; Jerison, David; Lieb, Elliott H. 41 1996 Continuity of the temperature in boundary heat control problems. Zbl 1190.35125Athanasopoulos, I.; Caffarelli, L. A. 40 2010 Allocation maps with general cost functions. Zbl 0883.49030Caffarelli, Luis A. 40 1996 Regularity of the free boundary in parabolic phase-transition problems. Zbl 0891.35164Athanasopoulos, I.; Caffarelli, L.; Salsa, S. 39 1996 Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems. Zbl 0853.35049Athanasopoulos, I.; Caffarelli, L.; Salsa, S. 39 1996 Smoothness and analyticity of free boundaries in variational inequalities. Zbl 0363.35009Caffarelli, L. A.; Riviere, N. M. 38 1976 Asymptotic estimates for the plasma problem. Zbl 0466.35033Caffarelli, Luis A.; Friedman, Avner 38 1980 How an initially stationary interface begins to move in porous medium flow. Zbl 0542.76119Aronson, D. G.; Caffarelli, L. A.; Kamin, S. 38 1983 Some remarks on singular solutions of nonlinear elliptic equations. III: Viscosity solutions including parabolic operators. Zbl 1279.35044Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis 37 2013 Regularity for \(C^{1, \alpha}\) interface transmission problems. Zbl 1467.35169Caffarelli, Luis Ángel; Soria-Carro, María; Stinga, Pablo Raúl 3 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 Optimal regularity and structure of the free boundary for minimizers in cohesive zone models. Zbl 1442.49005Caffarelli, L.; Cagnetti, F.; Figalli, A. 2 2020 Existence of weak solutions to a continuity equation with space time nonlocal Darcy law. Zbl 1459.35233Caffarelli, Luis; Gualdani, Maria; Zamponi, Nicola 2 2020 Minimal surfaces and free boundaries: recent developments. Zbl 1433.35464Caffarelli, Luis A.; Sire, Yannick 1 2020 Fully nonlinear integro-differential equations with deforming kernels. Zbl 1452.35055Caffarelli, Luis; Teymurazyan, Rafayel; Urbano, José Miguel 1 2020 Parabolic obstacle problems, quasi-convexity and regularity. Zbl 1432.35264Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil 5 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 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 3 2019 On the regularity of the non-dynamic parabolic fractional obstacle problem. Zbl 1394.35588Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil 15 2018 A minimization problem with free boundary related to a cooperative system. Zbl 1395.35226Caffarelli, Luis A.; Shahgholian, Henrik; Yeressian, Karen 10 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 Two-phase anisotropic free boundary problems and applications to the Bellman equation in 2D. Zbl 1393.35247Caffarelli, L.; De Silva, D.; Savin, O. 3 2018 Obstacle problems for integro-differential operators: regularity of solutions and free boundaries. Zbl 1371.35361Caffarelli, Luis; Ros-Oton, Xavier; Serra, Joaquim 33 2017 Porous medium flow with both a fractional potential pressure and fractional time derivative. Zbl 1372.35328Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 20 2017 On some pointwise inequalities involving nonlocal operators. Zbl 1482.35017Caffarelli, Luis A.; Sire, Yannick 15 2017 A logistic equation with nonlocal interactions. Zbl 1356.35261Caffarelli, Luis; Dipierro, Serena; Valdinoci, Enrico 14 2017 The two membranes problem for different operators. Zbl 1368.35045Caffarelli, L.; De Silva, D.; Savin, O. 13 2017 On a long range segregation model. Zbl 1386.35084Caffarelli, L.; Patrizi, S.; Quitalo, V. 5 2017 Fractional elliptic equations, Caccioppoli estimates and regularity. Zbl 1381.35211Caffarelli, Luis A.; Stinga, Pablo Raúl 90 2016 A parabolic problem with a fractional time derivative. Zbl 1338.35428Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 81 2016 A free boundary problem related to thermal insulation. Zbl 1351.35268Caffarelli, Luis A.; Kriventsov, Dennis 16 2016 The Dirichlet problem for stable-like operators and related probabilistic representations. Zbl 1352.60080Arapostathis, Ari; Biswas, Anup; Caffarelli, Luis 12 2016 Obstacle-type problems for minimal surfaces. Zbl 1370.35070Caffarelli, L.; De Silva, D.; Savin, O. 11 2016 Regularity of solutions of the fractional porous medium flow with exponent \(1/2\). Zbl 1335.35273Caffarelli, L.; Vázquez, J. L. 10 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 2 2015 Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities. Zbl 1296.35208Caffarelli, Luis; Jin, Tianling; Sire, Yannick; Xiong, Jingang 29 2014 Partial differential equation models in the socio-economic sciences. Zbl 1353.00004 13 2014 Hölder regularity for generalized master equations with rough kernels. Zbl 1312.45013Caffarelli, Luis; Silvestre, Luis 11 2014 On the asymptotic behavior of a Boltzmann-type price formation model. Zbl 1307.35302Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 8 2014 Counter-example in three dimension and homogenization of geometric motions in two dimension. Zbl 1293.35026Caffarelli, L. A.; Monneau, R. 5 2014 Regularity for anisotropic fully nonlinear integro-differential equations. Zbl 1304.35730Caffarelli, Luis A.; Leitão, Raimundo; Urbano, José Miguel 5 2014 A perturbation argument for a Monge-Ampère type equation arising in optimal transportation. Zbl 1294.35170Caffarelli, Luis; Del Mar González, María; Nguyen, Truyen 4 2014 Relations between geometric convexity, doubling measures and property \(\Gamma\). Zbl 1307.46006Caffarelli, Luis A.; Crandall, Michael G. 1 2014 Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088Caffarelli, Luis; Figalli, Alessio 51 2013 Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis 49 2013 Regularity properties of nonlocal minimal surfaces via limiting arguments. Zbl 1284.53008Caffarelli, Luis; Valdinoci, Enrico 48 2013 Some remarks on singular solutions of nonlinear elliptic equations. III: Viscosity solutions including parabolic operators. Zbl 1279.35044Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis 37 2013 On a Boltzmann-type price formation model. Zbl 1372.91039Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 17 2013 A priori bounds for solutions of a nonlocal evolution PDE. Zbl 1273.35067Caffarelli, Luis; Valdinoci, Enrico 6 2013 Non-local diffusions, drifts and games. Zbl 1266.35060Caffarelli, Luis 189 2012 Non-local gradient dependent operators. Zbl 1252.35099Bjorland, C.; Caffarelli, L.; Figalli, A. 54 2012 Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio 53 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 19 2012 Traveling waves for a boundary reaction-diffusion equation. Zbl 1255.35072Caffarelli, L.; Mellet, A.; Sire, Y. 8 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 113 2011 Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105Caffarelli, Luis; Vazquez, Juan Luis 98 2011 Uniform estimates and limiting arguments for nonlocal minimal surfaces. Zbl 1357.49143Caffarelli, Luis; Valdinoci, Enrico 82 2011 The Evans-Krylov theorem for nonlocal fully nonlinear equations. Zbl 1232.49043Caffarelli, Luis; Silvestre, Luis 72 2011 Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis 71 2011 Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043Caffarelli, Luis; Vázquez, Juan-Luis 43 2011 On a price formation free boundary model by Lasry and Lions. Zbl 1216.91012Caffarelli, Luis A.; Markowich, Peter A.; Pietschmann, Jan-F. 13 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 7 2011 Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063Caffarelli, Luis A.; Vasseur, Alexis 411 2010 Nonlocal minimal surfaces. Zbl 1248.53009Caffarelli, L.; Roquejoffre, J.-M.; Savin, O. 198 2010 Variational problems with free boundaries for the fractional Laplacian. Zbl 1221.35453Caffarelli, Luis A.; Roquejoffre, Jean-Michel; Sire, Yannick 135 2010 Free boundaries in optimal transport and Monge-Ampère obstacle problems. Zbl 1196.35231Caffarelli, Luis A.; McCann, Robert J. 46 2010 Rates of convergence for the homogenization of fully nonlinear uniformly elliptic PDE in random media. Zbl 1192.35048Caffarelli, Luis A.; Souganidis, Panagiotis E. 44 2010 Continuity of the temperature in boundary heat control problems. Zbl 1190.35125Athanasopoulos, I.; Caffarelli, L. A. 40 2010 Convergence of nonlocal threshold dynamics approximations to front propagation. Zbl 1190.65132Caffarelli, Luis A.; Souganidis, Panagiotis E. 35 2010 Distance functions and almost global solutions of eikonal equations. Zbl 1187.35024Caffarelli, Luis A.; Crandall, Michael G. 16 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. 16 2010 On the Evans-Krylov theorem. Zbl 1180.35229Caffarelli, Luis; Silvestre, Luis 8 2010 Analysis on the junctions of domain walls. Zbl 1193.35255Caffarelli, Luis A.; Lin, Fang Hua 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 267 2009 Some remarks on singular solutions of nonlinear elliptic equations. I. Zbl 1215.35068Caffarelli, Luis; Li, Yan Yan; Nirenberg, Louis 32 2009 The geometry of solutions to a segregation problem for nondivergence systems. Zbl 1217.35015Caffarelli, L. A.; Karakhanyan, A. L.; Lin, Fang-Hua 25 2009 Nonlocal heat flows preserving the \(L^2\) energy. Zbl 1154.35364Caffarelli, Luis; Lin, Fanghua 17 2009 Random homogenization of an obstacle problem. Zbl 1180.35069Caffarelli, L. A.; Mellet, A. 17 2009 Surfaces minimizing nonlocal energies. Zbl 1182.53055Caffarelli, Luis A. 10 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 267 2008 Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. Zbl 1194.35138Caffarelli, L. A.; Lin, Fang-Hua 67 2008 The structure of the free boundary for lower dimensional obstacle problems. Zbl 1185.35339Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. 58 2008 A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs. Zbl 1140.65075Caffarelli, Luis A.; Souganidis, Panagiotis E. 32 2008 Weak solutions of one inverse problem in geometric optics. Zbl 1202.78003Caffarelli, L. A.; Oliker, V. I. 24 2008 On the regularity of reflector antennas. Zbl 1140.35009Caffarelli, Luis A.; Gutiíerrez, Cristian E.; Huang, Qingbo 22 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 9 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 Some nonlinear problems involving nonlocal diffusions. Zbl 1419.35203Caffarelli, Luis A. 5 2008 Viscosity method for homogenization of highly oscillating obstacles. Zbl 1158.35109Caffarelli, Luis; Lee, Ki-Ahm 4 2008 An extension problem related to the fractional Laplacian. Zbl 1143.26002Caffarelli, Luis; Silvestre, Luis 1,361 2007 An optimal partition problem for eigenvalues. Zbl 1123.65060Cafferelli, L. A.; Lin, Fang Hua 54 2007 A constant rank theorem for solutions of fully nonlinear elliptic equations. Zbl 1191.35127Caffarelli, Luis A.; Guan, Pengfei; Ma, Xinan 30 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. 10 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. 3 2007 Free boundary problems for fractional powers of the Laplacian. Zbl 1253.35224Caffarelli, Luis 1 2007 Phase transitions: uniform regularity of the intermediate layers. Zbl 1090.49019Caffarelli, Luis A.; Córdoba, Antonio 20 2006 ...and 172 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 6,139 Authors 125 Caffarelli, Luis Ángel 111 Valdinoci, Enrico 78 Vazquez, Juan Luis 63 Wei, Juncheng 62 Byun, Sun-Sig 61 Shahgholian, Henrik 57 Wang, Lihe 53 Dipierro, Serena 50 Figalli, Alessio 50 Sire, Yannick 49 Savin, Ovidiu V. 48 Lin, Chang-Shou 48 Zhang, Binlin 44 Xiang, Mingqi 42 Quaas, Alexander 41 Ambrosio, Vincenzo 41 Lee, Ki-Ahm 39 Li, YanYan 37 Rădulescu, Vicenţiu D. 36 Wang, Xu-Jia 35 Bao, Jiguang 35 Dong, Hongjie 35 Friedman, Avner 35 Garofalo, Nicola 35 Teixeira, Eduardo V. O. 34 Farina, Alberto 33 Li, Dongsheng 31 Novaga, Matteo 31 Ros-Oton, Xavier 31 Rossi, Julio Daniel 31 Trudinger, Neil Sidney 30 Kim, Inwon Christina 29 Ferrari, Fausto 28 Kenig, Carlos Eduardo 28 Li, Congming 28 Squassina, Marco 27 Nyström, Kaj 27 Peral Alonso, Ireneo 27 Petrosyan, Arshak 27 Vitolo, Antonio 27 Weiss, Georg Sebastian 26 De Silva, Daniela 26 Kang, Dongsheng 26 Silvestre, Luis E. 25 Felmer, Patricio L. 25 González, María del Mar 25 Nochetto, Ricardo Horacio 25 Sciunzi, Berardino 25 Terracini, Susanna 24 Del Pino, Manuel A. 24 Dolbeault, Jean 24 Gutiérrez, Cristian E. 24 Ivochkina, Nina Mikhaĭlovna 24 Miyagaki, Olimpio Hiroshi 24 Musso, Monica 24 Seregin, Gregory A. 23 Abdellaoui, Boumediene 23 Chen, Wenxiong 23 Niu, Pengcheng 23 Serra Montolí, Joaquim 23 Zheng, Shenzhou 22 Dai, Limei 22 Hebey, Emmanuel 22 Sirakov, Boyan Slavchev 22 Velichkov, Bozhidar 22 Wang, Kelei 21 Bucur, Dorin 21 Lin, Fang Hua 21 Maldonado, Diego 21 Salsa, Sandro 21 Tang, Xianhua 21 Wolanski, Noemi I. 21 Yao, Fengping 21 Zou, Wenming 20 Banerjee, Agnid 20 Dai, Wei 20 Fall, Mouhamed Moustapha 20 Karakhanyan, Aram L. 20 Lu, Guozhen 20 Mingione, Giuseppe 20 Monneau, Régis 20 Musina, Roberta 20 Peng, Shuangjie 20 Salani, Paolo 20 Stinga, Pablo Raúl 20 Xiong, Jingang 20 Zhang, Lei 19 Birindelli, Isabeau 19 Bonforte, Matteo 19 Cabré, Xavier 19 Chen, Huyuan 19 da Silva, João Vítor 19 McCann, Robert J. 19 Shivaji, Ratnasingham 19 Wang, Yanqing 18 Chen, Caisheng 18 Chen, Zhen-Qing 18 Krylov, Nicolaĭ Vladimirovich 18 Liu, Jianguo 18 Molica Bisci, Giovanni ...and 6,039 more Authors all top 5 Cited in 488 Serials 543 Journal of Differential Equations 446 Nonlinear Analysis. 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(English Edition) 20 Memoirs of the American Mathematical Society 20 Journal of Dynamics and Differential Equations 20 Journal of Inequalities and Applications 20 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 20 SN Partial Differential Equations and Applications 19 International Journal of Mathematics 18 Rocky Mountain Journal of Mathematics 18 Indiana University Mathematics Journal 18 Physica D 18 Journal of Fixed Point Theory and Applications 17 Archiv der Mathematik 17 Bulletin of the American Mathematical Society. New Series 17 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 17 The Journal of Fourier Analysis and Applications 17 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 16 Mathematics of Computation 16 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 16 Stochastic Processes and their Applications 16 Bulletin des Sciences Mathématiques ...and 388 more Serials all top 5 Cited in 56 Fields 7,295 Partial differential equations (35-XX) 1,074 Fluid mechanics (76-XX) 1,035 Calculus of variations and optimal control; optimization (49-XX) 625 Differential geometry (53-XX) 508 Global analysis, analysis on manifolds (58-XX) 473 Operator theory (47-XX) 456 Numerical analysis (65-XX) 390 Real functions (26-XX) 363 Probability theory and stochastic processes (60-XX) 358 Functional analysis (46-XX) 259 Potential theory (31-XX) 234 Integral equations (45-XX) 190 Harmonic analysis on Euclidean spaces (42-XX) 184 Mechanics of deformable solids (74-XX) 167 Statistical mechanics, structure of matter (82-XX) 139 Convex and discrete geometry (52-XX) 131 Several complex variables and analytic spaces (32-XX) 126 Ordinary differential equations (34-XX) 121 Classical thermodynamics, heat transfer (80-XX) 121 Quantum theory (81-XX) 114 Biology and other natural sciences (92-XX) 107 Measure and integration (28-XX) 92 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 88 Systems theory; control (93-XX) 85 Dynamical systems and ergodic theory (37-XX) 78 Geophysics (86-XX) 60 Operations research, mathematical programming (90-XX) 59 Functions of a complex variable (30-XX) 56 Optics, electromagnetic theory (78-XX) 31 Topological groups, Lie groups (22-XX) 30 Difference and functional equations (39-XX) 28 Abstract harmonic analysis (43-XX) 28 Astronomy and astrophysics (85-XX) 27 Mechanics of particles and systems (70-XX) 26 Approximations and expansions (41-XX) 25 Linear and multilinear algebra; matrix theory (15-XX) 25 Relativity and gravitational theory (83-XX) 22 Statistics (62-XX) 20 Computer science (68-XX) 18 Special functions (33-XX) 15 Geometry (51-XX) 13 General and overarching topics; collections (00-XX) 13 Algebraic geometry (14-XX) 13 Integral transforms, operational calculus (44-XX) 13 Information and communication theory, circuits (94-XX) 11 Combinatorics (05-XX) 7 History and biography (01-XX) 7 General topology (54-XX) 6 Number theory (11-XX) 6 Manifolds and cell complexes (57-XX) 5 Algebraic topology (55-XX) 4 Nonassociative rings and algebras (17-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Group theory and generalizations (20-XX) 2 Sequences, series, summability (40-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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