## 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. 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
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### 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
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### 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
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### 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)

### 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 1143.26002
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 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
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
Interior $$W^{2,p}$$ estimates for solutions of the Monge-Ampère equation. Zbl 0704.35044
Caffarelli, Luis A.
1990
Nonlocal minimal surfaces. Zbl 1248.53009
Caffarelli, L.; Roquejoffre, J.-M.; Savin, O.
2010
Non-local diffusions, drifts and games. Zbl 1266.35060
Caffarelli, Luis
2012
Variational problems with two phases and their free boundary. Zbl 0844.35137
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
1984
The obstacle problem revisited. Zbl 0928.49030
Caffarelli, L. A.
1998
A geometric approach to free boundary problems. Zbl 1083.35001
Caffarelli, Luis; Salsa, Sandro
2005
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
Boundary behavior of nonnegative solutions of elliptic operators in divergence form. Zbl 0512.35038
Caffarelli, L.; Fabes, E.; Mortola, S.; Salsa, S.
1981
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
A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity. Zbl 0704.35045
Caffarelli, L. A.
1990
Monotonicity for elliptic equations in unbounded Lipschitz domains. Zbl 0906.35035
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1997
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
The regularity of mappings with a convex potential. Zbl 0753.35031
Caffarelli, Luis A.
1992
Regularity results for nonlocal equations by approximation. Zbl 1231.35284
Caffarelli, Luis; Silvestre, Luis
2011
Vortex condensation in the Chern-Simons Higgs model: An existence theorem. Zbl 0846.58063
Caffarelli, Luis A.; Yang, Yisong
1995
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. I: Lipschitz free boundaries are $$C^{1,\alpha}$$. Zbl 0676.35085
Caffarelli, Luis A.
1987
A Harnack inequality approach to the regularity of free boundaries. II: Flat free boundaries are Lipschitz. Zbl 0676.35086
Caffarelli, Luis A.
1989
Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105
Caffarelli, Luis; Vazquez, Juan Luis
2011
Convexity of solutions of semilinear elliptic equations. Zbl 0599.35065
Caffarelli, Luis A.; Friedman, Avner
1985
Convexity properties of solutions to some classical variational problems. Zbl 0508.49013
Caffarelli, Luis A.; Spruck, Joel
1982
Fractional elliptic equations, Caccioppoli estimates and regularity. Zbl 1381.35211
Caffarelli, Luis A.; Stinga, Pablo Raúl
2016
Boundary regularity of maps with convex potentials. II. Zbl 0916.35016
Caffarelli, Luis A.
1996
Inequalities for second-order elliptic equations with applications to unbounded domains. I. Zbl 0860.35004
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1996
The initial trace of a solution of the porous medium equation. Zbl 0556.76084
Aronson, D. G.; Caffarelli, L. A.
1983
Uniform estimates and limiting arguments for nonlocal minimal surfaces. Zbl 1357.49143
Caffarelli, Luis; Valdinoci, Enrico
2011
A parabolic problem with a fractional time derivative. Zbl 1338.35428
Allen, Mark; Caffarelli, Luis; Vasseur, Alexis
2016
Properties of the solutions of the linearized Monge-Ampère equation. Zbl 0878.35039
Caffarelli, Luis A.; Gutiérrez, Cristian E.
1997
Boundary regularity of maps with convex potentials. Zbl 0778.35015
Caffarelli, Luis A.
1992
Regularity of the free boundary of a gas flow in an $$n$$-dimensional porous medium. Zbl 0439.76085
Caffarelli, Luis A.; Friedman, Avner
1980
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
Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. Zbl 1194.35138
Caffarelli, L. A.; Lin, Fang-Hua
2008
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
Continuity of the temperature in the two-phase Stefan problem. Zbl 0516.35080
Caffarelli, L. A.; Evans, L. C.
1983
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
Regularity of a free boundary with application to the Pompeiu problem. Zbl 0960.35112
Caffarelli, Luis A.; Karp, Lavi; Shahgholian, Henrik
2000
An extension to a theorem of Jörgens, Calabi, and Pogorelov. Zbl 1236.35041
Caffarelli, L.; Li, YanYan
2003
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
Monotonicity properties of optimal transportation and the FKG and related inequalities. Zbl 0978.60107
Caffarelli, Luis A.
2000
The structure of the free boundary for lower dimensional obstacle problems. Zbl 1185.35339
Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S.
2008
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
An $$L^ \infty$$ bound for solutions of the Cahn-Hilliard equation. Zbl 0851.35010
Caffarelli, Luis A.; Muler, Nora E.
1995
Uniform estimates for regularization of free boundary problems. Zbl 0702.35252
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1990
Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations. Zbl 0593.35047
Caffarelli, Luis A.; Friedman, Avner
1985
An optimal partition problem for eigenvalues. Zbl 1123.65060
Cafferelli, L. A.; Lin, Fang Hua
2007
Some new monotonicity theorems with applications to free boundary problems. Zbl 1142.35382
Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E.
2002
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.; Villani, Cédric
2003
A free boundary problem for quasi-linear elliptic equations. Zbl 0554.35129
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
1984
Non-local gradient dependent operators. Zbl 1252.35099
Bjorland, C.; Caffarelli, L.; Figalli, A.
2012
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
Uniform convergence of a singular perturbation problem. Zbl 0829.49013
Caffarelli, Luis A.; Córdoba, Antonio
1995
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
Completely singular elliptic-harmonic measures. Zbl 0482.35020
Caffarelli, Luis A.; Fabes, Eugene B.; Kenig, Carlos E.
1981
Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088
Caffarelli, Luis; Figalli, Alessio
2013
A free-boundary problem for the heat equation arising in flame propagation. Zbl 0814.35149
Caffarelli, Luis A.; Vázquez, Juan L.
1995
A gradient bound for entire solutions of quasi-linear equations and its consequences. Zbl 0819.35016
Caffarelli, Luis; Garofalo, Nicola; Segala, Fausto
1994
Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312
Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis
2013
Compactness methods in free boundary problems. Zbl 0437.35070
Caffarelli, Luis A.
1980
Regularity properties of nonlocal minimal surfaces via limiting arguments. Zbl 1284.53008
Caffarelli, Luis; Valdinoci, Enrico
2013
Optimal regularity of lower dimensional obstacle problems. Zbl 1108.35038
Athanasopoulos, I.; Caffarelli, L. A.
2004
Free boundaries in optimal transport and Monge-Ampère obstacle problems. Zbl 1196.35231
Caffarelli, Luis A.; McCann, Robert J.
2010
Continuity of the density of a gas flow in a porous medium. Zbl 0425.35060
Caffarelli, Luis A.; Friedman, Avner
1979
Potential methods in variational inequalities. Zbl 0455.49010
Caffarelli, L. A.; Kinderlehrer, D.
1980
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
Regularity of a free boundary in parabolic potential theory. Zbl 1054.35142
Caffarelli, Luis; Petrosyan, Arshak; Shahgholian, Henrik
2004
Real analysis related to the Monge-Ampère equation. Zbl 0858.35034
Caffarelli, Luis A.; Gutiérrez, Cristian E.
1996
Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043
Caffarelli, Luis; Vázquez, Juan-Luis
2011
Nonlinear second order elliptic equations. IV. Starshaped compact Weingarten hypersurfaces. Zbl 0672.35027
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1986
Symmetry for elliptic equations in a half space. Zbl 0793.35034
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1993
Planelike minimizers in periodic media. Zbl 1036.49040
Caffarelli, Luis A.; de la Llave, Rafael
2001
The blow-up boundary for nonlinear wave equations. Zbl 0638.35053
Caffarelli, Luis A.; Friedman, Avner
1986
An optimization problem with volume constraint. Zbl 0588.49005
Aguilera, N.; Alt, H. W.; Caffarelli, L. A.
1986
On the case of equality in the Brunn-Minkowski inequality for capacity. Zbl 0847.31005
Caffarelli, Luis A.; Jerison, David; Lieb, Elliott H.
1996
Continuity of the temperature in boundary heat control problems. Zbl 1190.35125
Athanasopoulos, I.; Caffarelli, L. A.
2010
Allocation maps with general cost functions. Zbl 0883.49030
Caffarelli, Luis A.
1996
Regularity of the free boundary in parabolic phase-transition problems. Zbl 0891.35164
Athanasopoulos, I.; Caffarelli, L.; Salsa, S.
1996
Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems. Zbl 0853.35049
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
Asymptotic estimates for the plasma problem. Zbl 0466.35033
Caffarelli, Luis A.; Friedman, Avner
1980
How an initially stationary interface begins to move in porous medium flow. Zbl 0542.76119
Aronson, D. G.; Caffarelli, L. A.; Kamin, S.
1983
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
Regularity for $$C^{1, \alpha}$$ interface transmission problems. Zbl 1467.35169
Caffarelli, Luis Ángel; Soria-Carro, María; Stinga, Pablo Raúl
2021
The leading edge of a free boundary interacting with a line of fast diffusion. Zbl 1465.35414
Caffarelli, L. A.; Roquejoffre, J.-M.
2021
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
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
Parabolic obstacle problems, quasi-convexity and regularity. Zbl 1432.35264
Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil
2019
Interior regularity for fractional systems. Zbl 1411.35111
Caffarelli, Luis; Dávila, Gonzalo
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
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 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 1482.35017
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
The Dirichlet problem for stable-like operators and related probabilistic representations. Zbl 1352.60080
Arapostathis, Ari; Biswas, Anup; Caffarelli, Luis
2016
Obstacle-type problems for minimal surfaces. Zbl 1370.35070
Caffarelli, L.; De Silva, D.; Savin, O.
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
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
Counter-example in three dimension and homogenization of geometric motions in two dimension. Zbl 1293.35026
Caffarelli, L. A.; Monneau, R.
2014
Regularity for anisotropic fully nonlinear integro-differential equations. Zbl 1304.35730
Caffarelli, Luis A.; Leitão, Raimundo; Urbano, José Miguel
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 to the parabolic fractional obstacle problem. Zbl 1277.35088
Caffarelli, Luis; Figalli, Alessio
2013
Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312
Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis
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
Non-local gradient dependent operators. Zbl 1252.35099
Bjorland, C.; Caffarelli, L.; Figalli, A.
2012
Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278
Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio
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
Distance functions and almost global solutions of eikonal equations. Zbl 1187.35024
Caffarelli, Luis A.; Crandall, Michael G.
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
On the Evans-Krylov theorem. Zbl 1180.35229
Caffarelli, Luis; Silvestre, Luis
2010
Analysis on the junctions of domain walls. Zbl 1193.35255
Caffarelli, Luis A.; Lin, Fang Hua
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
Some nonlinear problems involving nonlocal diffusions. Zbl 1419.35203
Caffarelli, Luis A.
2008
Viscosity method for homogenization of highly oscillating obstacles. Zbl 1158.35109
Caffarelli, Luis; Lee, Ki-Ahm
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
...and 172 more Documents
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### 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
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### Cited in 488 Serials

 543 Journal of Differential Equations 446 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 445 Calculus of Variations and Partial Differential Equations 320 Journal of Mathematical Analysis and Applications 277 Journal of Functional Analysis 272 Communications in Partial Differential Equations 257 Archive for Rational Mechanics and Analysis 199 Advances in Mathematics 193 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 185 Discrete and Continuous Dynamical Systems 163 Transactions of the American Mathematical Society 141 Communications on Pure and Applied Analysis 135 Proceedings of the American Mathematical Society 131 Journal de Mathématiques Pures et Appliquées. Neuvième Série 120 Mathematische Annalen 118 Communications in Mathematical Physics 109 The Journal of Geometric Analysis 101 SIAM Journal on Mathematical Analysis 95 Communications in Contemporary Mathematics 93 Annali di Matematica Pura ed Applicata. Serie Quarta 81 Communications on Pure and Applied Mathematics 79 Journal of Mathematical Sciences (New York) 74 NoDEA. Nonlinear Differential Equations and Applications 73 Complex Variables and Elliptic Equations 72 Potential Analysis 72 Advanced Nonlinear Studies 67 Journal of Mathematical Physics 61 Boundary Value Problems 60 Applied Mathematics Letters 58 Mathematische Zeitschrift 57 Duke Mathematical Journal 55 Advances in Nonlinear Analysis 52 Applicable Analysis 52 Computers & Mathematics with Applications 52 Manuscripta Mathematica 52 Nonlinear Analysis. Theory, Methods & Applications 51 Journal of Mathematical Fluid Mechanics 48 Mathematical Methods in the Applied Sciences 48 Revista Matemática Iberoamericana 48 Comptes Rendus. Mathématique. Académie des Sciences, Paris 47 Science China. Mathematics 46 Journal of the European Mathematical Society (JEMS) 46 Nonlinear Analysis. Real World Applications 44 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 43 Nonlinearity 42 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 42 Applied Mathematics and Optimization 41 ZAMP. Zeitschrift für angewandte Mathematik und Physik 40 Journal d’Analyse Mathématique 40 Journal of Scientific Computing 38 Inventiones Mathematicae 37 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 37 Acta Mathematica Sinica. English Series 37 Discrete and Continuous Dynamical Systems. Series B 37 Discrete and Continuous Dynamical Systems. Series S 36 Chinese Annals of Mathematics. Series B 36 Journal of Evolution Equations 32 Journal of Computational Physics 30 Acta Applicandae Mathematicae 30 Mathematics in Engineering 28 Numerische Mathematik 28 Milan Journal of Mathematics 27 Journal of Computational and Applied Mathematics 27 SIAM Journal on Numerical Analysis 27 Analysis & PDE 26 Advances in Calculus of Variations 25 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 25 St. Petersburg Mathematical Journal 24 Acta Mathematica 24 Electronic Journal of Differential Equations (EJDE) 24 Fractional Calculus & Applied Analysis 23 Applied Mathematics and Computation 23 Journal of the American Mathematical Society 23 Topological Methods in Nonlinear Analysis 22 Journal für die Reine und Angewandte Mathematik 22 Abstract and Applied Analysis 22 Mediterranean Journal of Mathematics 21 Israel Journal of Mathematics 21 SIAM Journal on Scientific Computing 21 Interfaces and Free Boundaries 21 Acta Mathematica Scientia. Series B. (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
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### 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)

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