Edit Profile (opens in new tab) Lions, Pierre-Louis Co-Author Distance Author ID: lions.pierre-louis Published as: Lions, Pierre-Louis; Lions, P. L.; Lions, P.-L.; Lions, Pierre Louis more...less Homepage: https://www.college-de-france.fr/site/pierre-louis-lions/ External Links: MacTutor · MGP · Wikidata · dblp · GND · IdRef · theses.fr Awards: Fields Medal (1994) Documents Indexed: 378 Publications since 1977, including 9 Books 7 Contributions as Editor Reviewing Activity: 1 Review Biographic References: 4 Publications Co-Authors: 114 Co-Authors with 263 Joint Publications 3,990 Co-Co-Authors all top 5 Co-Authors 117 single-authored 36 Souganidis, Panagiotis E. 33 Lasry, Jean-Michel 27 Le Bris, Claude 22 Crandall, Michael G. 15 Blanc, Xavier 14 Perthame, Benoît 12 Berestycki, Henri 12 Catto, Isabelle 11 DiPerna, Ronald J. 10 Alvino, Angelo 10 Masmoudi, Nader 10 Trombetti, Guido 6 Esteban, Maria J. 6 Morel, Jean-Michel 5 Achdou, Yves 5 Bahri, Abbas 5 Bertucci, Charles 5 Ishii, Hitoshi 4 Arisawa, Mariko 4 Barles, Guy 4 Brézis, Haïm 4 Cardaliaguet, Pierre 4 Evans, Lawrence Craig 4 Guichard, Frédéric 4 Menaldi, Jose-Luis 4 Meyer, Yves F. 3 Coifman, Ronald Raphaël 3 Guedes de Figueiredo, Djairo 3 Díaz Díaz, Jesús Ildefonso 3 Fournié, Eric 3 Moll, Benjamin 3 Musiela, Marek 3 Quarteroni, Alfio M. 3 Semmes, Stephen W. 3 Tadmor, Eitan 3 Trudinger, Neil Sidney 2 Caglioti, Emanuele 2 Capuzzo Dolcetta, Italo 2 Cazenave, Thierry 2 Gassiat, Paul 2 Gogny, D. 2 Marchioro, Carlo 2 Nussbaum, Roger David 2 Pacella, Filomena 2 Porretta, Alessio 2 Pulvirenti, Mario 2 Seeger, Benjamin 2 Sznitman, Alain-Sol 2 Toscani, Giuseppe 2 Urbas, John Ivan Eugene 1 Alziary, Bénédicte 1 Bensoussan, Alain 1 Buera, Francisco J. 1 Cancès, Eric 1 Catté, Francine 1 Chambolle, Antonin 1 Chan, Tony Fan-Cheong 1 Coll, Tomeu 1 Coron, Jean-Michel 1 Coti Zelati, Vittorio 1 Da Lio, Francesca 1 Darves-Bornoz, J. M. 1 Debbah, Mérouane 1 Delarue, François 1 Desjardins, Benoît 1 Duffie, James Darrell 1 Ekeland, Ivar 1 Ferone, Vincenzo 1 Fleming, Wendell Helms 1 Friedman, Avner 1 Friz, Peter Karl 1 Fusco, Nicola 1 Gabaix, Xavier 1 Gallagher, Isabelle 1 Gallay, Thierry 1 Gess, Benjamin 1 Gimbert, P. 1 Giraud, Pierre-Noel 1 Golse, François 1 Grenier, Emmanuel 1 Guéant, Olivier 1 Han, Jiequn 1 Hauray, Maxime 1 Hou, Thomas Yizhao 1 Jensen, Reed 1 Kocan, Maciej 1 Kutev, Nikolai D. 1 Lachapelle, Aime 1 Larrouturou, Bernard 1 Laurière, Mathieu 1 Lebuchous, Jérôme 1 Lebuchoux, Jérôme 1 Lehalle, Charles-Albert 1 Majda, Andrew J. 1 Mas-Gallic, Sylvie 1 Matarasso, Silvano 1 Motet, Gilles 1 Nečas, Jindřich 1 Netuka, Ivan 1 Nisio, Makiko ...and 14 more Co-Authors all top 5 Serials 37 Comptes Rendus de l’Académie des Sciences. Série I 18 Communications in Partial Differential Equations 17 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 15 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 14 Comptes Rendus. Mathématique. Académie des Sciences, Paris 12 Archive for Rational Mechanics and Analysis 12 Journal de Mathématiques Pures et Appliquées. Neuvième Série 12 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 11 Journal of Functional Analysis 9 Communications on Pure and Applied Mathematics 8 Nonlinear Analysis. Theory, Methods & Applications 7 Communications in Mathematical Physics 6 Indiana University Mathematics Journal 6 SIAM Journal on Control and Optimization 5 Proceedings of the American Mathematical Society 5 Ricerche di Matematica 5 Revista Matemática Iberoamericana 4 Numerische Mathematik 4 SIAM Journal on Numerical Analysis 4 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 3 Israel Journal of Mathematics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Journal of Differential Equations 3 Transactions of the American Mathematical Society 3 Differential and Integral Equations 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Finance and Stochastics 3 Computing and Visualization in Science 3 Stochastic and Partial Differential Equations. Analysis and Computations 2 Applicable Analysis 2 Journal d’Analyse Mathématique 2 Stochastics 2 Acta Mathematica 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Applied Mathematics and Optimization 2 Inventiones Mathematicae 2 Journal of Mathematics of Kyoto University 2 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 2 Bulletin of the American Mathematical Society. New Series 2 Bollettino della Unione Matematica Italiana. Series V. A 2 Oxford Lecture Series in Mathematics and its Applications 2 Networks and Heterogeneous Media 1 Computer Methods in Applied Mechanics and Engineering 1 Nonlinearity 1 Mathematics of Computation 1 Annales de l’Institut Fourier 1 Boletim da Sociedade Brasileira de Matemática 1 Calcolo 1 Commentationes Mathematicae Universitatis Carolinae 1 Duke Mathematical Journal 1 Econometrica 1 Gazette des Mathématiciens 1 Illinois Journal of Mathematics 1 Journal of Mathematical Economics 1 Journal of the Mathematical Society of Japan 1 Journal of Optimization Theory and Applications 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Mathematische Nachrichten 1 Mathematische Zeitschrift 1 Proceedings of the Japan Academy. Series A 1 RAIRO. Analyse Numérique 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 The Review of Economic Studies 1 Rendiconti del Seminario Matematico 1 Delft Progress Report 1 Chinese Annals of Mathematics. Series B 1 Acta Applicandae Mathematicae 1 Physica D 1 Probability Theory and Related Fields 1 Journal of the American Mathematical Society 1 Asymptotic Analysis 1 SIAM Review 1 Philosophical Transactions of the Royal Society of London. Series A 1 Séminaire Équations aux Dérivées Partielles 1 Electronic Journal of Differential Equations (EJDE) 1 Discrete and Continuous Dynamical Systems 1 Nonlinear Studies 1 Communications in Applied Analysis 1 Bollettino della Unione Matematica Italiana. Serie VIII. Sezione B. Articoli di Ricerca Matematica 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Annals of Mathematics. Second Series 1 Milan Journal of Mathematics 1 Communications in Mathematical Sciences 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Annals of Mathematics Studies 1 The IMA Volumes in Mathematics and its Applications 1 Lecture Notes in Mathematics 1 Pitman Research Notes in Mathematics Series 1 Mathematics and Financial Economics 1 Japanese Journal of Mathematics. 3rd Series 1 Research in the Mathematical Sciences 1 Séminaire Laurent Schwartz. EDP et Applications 1 Research Notes in Mathematics (San Francisco) 1 De Gruyter Series in Applied and Numerical Mathematics 1 Oxford Mathematical Monographs all top 5 Fields 273 Partial differential equations (35-XX) 97 Calculus of variations and optimal control; optimization (49-XX) 62 Fluid mechanics (76-XX) 50 Probability theory and stochastic processes (60-XX) 39 Systems theory; control (93-XX) 37 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 33 Statistical mechanics, structure of matter (82-XX) 28 Functional analysis (46-XX) 25 Operator theory (47-XX) 24 Quantum theory (81-XX) 23 Numerical analysis (65-XX) 13 Global analysis, analysis on manifolds (58-XX) 10 Ordinary differential equations (34-XX) 10 Mechanics of particles and systems (70-XX) 9 Computer science (68-XX) 7 General and overarching topics; collections (00-XX) 7 Integral equations (45-XX) 7 Mechanics of deformable solids (74-XX) 7 Operations research, mathematical programming (90-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Astronomy and astrophysics (85-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Statistics (62-XX) 3 Information and communication theory, circuits (94-XX) 2 Real functions (26-XX) 2 Convex and discrete geometry (52-XX) 2 Algebraic topology (55-XX) 1 History and biography (01-XX) 1 Difference and functional equations (39-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 358 Publications have been cited 28,581 times in 18,317 Documents Cited by ▼ Year ▼ User’s guide to viscosity solutions of second order partial differential equations. Zbl 0755.35015Crandall, Michael G.; Ishii, Hitoshi; Lions, Pierre-Louis 2,008 1992 Nonlinear scalar field equations. I: Existence of a ground state. Zbl 0533.35029Berestycki, Henri; Lions, Pierre-Louis 1,231 1983 The concentration-compactness principle in the calculus of variations. The locally compact case. I. Zbl 0541.49009Lions, Pierre-Louis 1,059 1984 The concentration-compactness principle in the calculus of variations. The locally compact case. II. Zbl 0704.49004Lions, P.-L. 974 1984 The concentration-compactness principle in the calculus of variations. The limit case. I. Zbl 0704.49005Lions, P.-L. 922 1985 Ordinary differential equations, transport theory and Sobolev spaces. Zbl 0696.34049DiPerna, R. J.; Lions, P. L. 920 1989 Viscosity solutions of Hamilton-Jacobi equations. Zbl 0599.35024Crandall, Michael G.; Lions, Pierre-Louis 912 1983 Mean field games. Zbl 1156.91321Lasry, Jean-Michel; Lions, Pierre-Louis 833 2007 Splitting algorithms for the sum of two nonlinear operators. Zbl 0426.65050Lions, Pierre-Louis; Mercier, B. 765 1979 On the Cauchy problem for Boltzmann equations: Global existence and weak stability. Zbl 0698.45010DiPerna, R. J.; Lions, P. L. 566 1989 Mathematical topics in fluid mechanics. Vol. 2: Compressible models. Zbl 0908.76004Lions, Pierre-Louis 523 1998 Mathematical topics in fluid mechanics. Vol. 1: Incompressible models. Zbl 0866.76002Lions, Pierre-Louis 522 1996 Orbital stability of standing waves for some nonlinear Schrödinger equations. Zbl 0513.35007Cazenave, T.; Lions, Pierre-Louis 490 1982 The concentration-compactness principle in the calculus of variations. The limit case. II. Zbl 0704.49006Lions, P.-L. 483 1985 Image recovery via total variation minimization and related problems. Zbl 0874.68299Chambolle, Antonin; Lions, Pierre-Louis 418 1997 Some properties of viscosity solutions of Hamilton-Jacobi equations. Zbl 0543.35011Crandall, M. G.; Evans, L. C.; Lions, Pierre-Louis 411 1984 Mean field games. I: The stationary case. (Jeux à champ moyen. I: Le cas stationnaire.) Zbl 1153.91009Lasry, Jean-Michel; Lions, Pierre-Louis 383 2006 Compensated compactness and Hardy spaces. Zbl 0864.42009Coifman, R.; Lions, P. L.; Meyer, Y.; Semmes, S. 379 1993 Mean field games. II: Finite horizon and optimal control. (Jeux à champ moyen. II: Horizon fini et contrôle optimal.) Zbl 1153.91010Lasry, Jean-Michel; Lions, Pierre-Louis 352 2006 The Choquard equation and related questions. Zbl 0453.47042Lions, Pierre-Louis 343 1980 Stochastic differential equations with reflecting boundary conditions. Zbl 0598.60060Lions, Pierre-Louis; Sznitman, A. S. 340 1984 On the existence of positive solutions of semilinear elliptic equations. Zbl 0511.35033Lions, Pierre-Louis 317 1982 Generalized solutions of Hamilton-Jacobi equations. Zbl 0497.35001Lions, Pierre-Louis 315 1982 Nonlinear scalar field equations. II: Existence of infinitely many solutions. Zbl 0556.35046Berestycki, Henri; Lions, Pierre-Louis 311 1983 Solutions of Hartree-Fock equations for Coulomb systems. Zbl 0618.35111Lions, P. L. 276 1987 Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. Zbl 0708.35031Ishii, H.; Lions, P. L. 261 1990 Propagation of moments and regularity for the 3-dimensional Vlasov- Poisson system. Zbl 0741.35061Lions, P. L.; Perthame, B. 253 1991 Image selective smoothing and edge detection by nonlinear diffusion. Zbl 0746.65091Catté, Francine; Lions, Pierre-Louis; Morel, Jean-Michel; Coll, Tomeu 246 1992 On Wigner measures. (Sur les mesures de Wigner.) Zbl 0801.35117Lions, Pierre Louis; Paul, Thierry 228 1993 Symétrie et compacité dans les espaces de Sobolev. Zbl 0501.46032Lions, Pierre-Louis 228 1982 A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description. Zbl 0745.76001Caglioti, E.; Lions, P. L.; Marchioro, C.; Pulvirenti, M. 228 1992 A priori estimates and existence of positive solutions of semilinear elliptic equations. Zbl 0452.35030de Figueiredo, D. G.; Lions, Pierre-Louis; Nussbaum, R. D. 227 1982 A kinetic formulation of multidimensional scalar conservation laws and related equations. Zbl 0820.35094Lions, P. L.; Perthame, B.; Tadmor, E. 214 1994 Regularity of the moments of the solution of a transport equation. Zbl 0652.47031Golse, François; Lions, Pierre-Louis; Perthame, Benoît; Sentis, Rémi 213 1988 Incompressible limit for a viscous compressible fluid. Zbl 0909.35101Lions, P.-L.; Masmoudi, N. 199 1998 Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. II: Viscosity solutions and uniqueness. Zbl 0716.49023Lions, P.-L. 193 1983 Two approximations of solutions of Hamilton-Jacobi equations. Zbl 0556.65076Crandall, M. G.; Lions, Pierre-Louis 177 1984 Image selective smoothing and edge detection by nonlinear diffusion. II. Zbl 0766.65117Alvarez, Luis; Lions, Pierre-Louis; Morel, Jean-Michel 174 1992 Global weak solutions of Vlasov-Maxwell systems. Zbl 0698.35128DiPerna, R. J.; Lions, P. L. 174 1989 Axioms and fundamental equations of image processing. Zbl 0788.68153Alvarez, Luis; Guichard, Frédéric; Lions, Pierre-Louis; Morel, Jean- Michel 164 1993 Kinetic formulation of the isentropic gas dynamics and \(p\)-systems. Zbl 0799.35151Lions, P. L.; Perthame, B.; Tadmor, E. 163 1994 Approximation de points fixes de contractions. Zbl 0349.47046Lions, Pierre-Louis 160 1977 On the Schwarz alternating method. I. Zbl 0658.65090Lions, P. L. 158 1988 Applications of Malliavin calculus to Monte Carlo methods in finance. Zbl 0947.60066Fournié, Eric; Lasry, Jean-Michel; Lebuchous, Jérôme; Lions, Pierre-Louis 156 1999 On the existence of a positive solution of semilinear elliptic equations in unbounded domains. Zbl 0883.35045Bahri, Abbas; Lions, Pierre-Louis 155 1997 Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates. Zbl 0853.76077Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E. 153 1996 A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description. II. Zbl 0840.76002Caglioti, E.; Lions, P. L.; Marchioro, C.; Pulvirenti, M. 152 1995 Global solutions for some Oldroyd models of non-Newtonian flows. Zbl 0957.35109Lions, P. L.; Masmoudi, N. 151 2000 Existence and non-existence results for semilinear elliptic problems in unbounded domains. Zbl 0506.35035Esteban, M. J.; Lions, Pierre-Louis 150 1982 Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints. I: The model problem. Zbl 0688.49026Lasry, J. M.; Lions, P. L. 148 1989 Produits infinis de resolvantes. Zbl 0387.47038Brézis, Haïm; Lions, Pierre-Louis 145 1978 An ODE approach to the existence of positive solutions for semilinear problems in \(R^ n\). Zbl 0522.35036Berestycki, Henri; Lions, Pierre-Louis; Peletier, L. A. 136 1981 From the Boltzmann equations to the equations of incompressible fluid mechanics. I, II. Zbl 0987.76088Lions, P.-L.; Masmoudi, N. 126 2001 Mean field games and applications. Zbl 1205.91027Guéant, Olivier; Lasry, Jean-Michel; Lions, Pierre-Louis 122 2011 The master equation and the convergence problem in mean field games. Zbl 1430.91002Cardaliaguet, Pierre; Delarue, François; Lasry, Jean-Michel; Lions, Pierre-Louis 114 2019 On the Schwarz alternating method. III: A variant for nonoverlapping subdomains. Zbl 0704.65090Lions, P. L. 111 1990 Morse index of some min-max critical points. I: Application to multiplicity results. Zbl 0645.58013Bahri, A.; Lions, P. L. 109 1988 Convex symmetrization and applications. Zbl 0877.35040Alvino, Angelo; Ferone, Vincenzo; Trombetti, Guido; Lions, Pierre-Louis 107 1997 A remark on regularization in Hilbert spaces. Zbl 0631.49018Lasry, J. M.; Lions, P. L. 106 1986 Asymptotic behavior of some nonlinear heat equations. Zbl 1194.35459Lions, P. L. 105 1982 Existence and uniqueness of solutions to Fokker-Planck type equations with irregular coefficients. Zbl 1157.35301Le Bris, C.; Lions, P.-L. 103 2008 On optimization problems with prescribed rearrangements. Zbl 0678.49003Alvino, Angelo; Trombetti, Guido; Lions, Pierre-Louis 102 1989 From molecular models to continuum mechanics. Zbl 1028.74005Blanc, X.; Le Bris, C.; Lions, P.-L. 99 2002 Résolution de problèmes elliptiques quasilineaires. Zbl 0449.35036Lions, Pierre-Louis 99 1980 Hamilton-Jacobi equations with state constraints. Zbl 0702.49019Capuzzo-Dolcetta, I.; Lions, Pierre-Louis 99 1990 Solutions of superlinear elliptic equations and their Morse indices. Zbl 0801.35026Bahri, A.; Lions, P. L. 97 1992 Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions. Zbl 0992.35067Desjardins, B.; Grenier, E.; Lions, P.-L.; Masmoudi, N. 93 1999 Compactness in Boltzmann’s equation via Fourier integral operators and applications. I, II. Zbl 0831.35139Lions, P. L. 92 1994 Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. I: The dynamic programming principle and applications. Zbl 0716.49022Lions, P.-L. 92 1983 \(L^ p\) regularity of velocity averages. Zbl 0763.35014DiPerna, R. J.; Lions, P. L.; Meyer, Y. 91 1991 Convex viscosity solutions and state constraints. Zbl 0890.49013Alvarez, O.; Lasry, J.-M.; Lions, P.-L. 87 1997 Isolated singularities in semilinear problems. Zbl 0458.35033Lions, Pierre-Louis 80 1980 Applications of Malliavin calculus to Monte-Carlo methods in finance. II. Zbl 0973.60061Fournié, Eric; Lasry, Jean-Michel; Lebuchoux, Jérôme; Lions, Pierre-Louis 79 2001 Solutions globales d’équations de la chaleur semi linéaires. (Global solutions of semi-linear heat equations). Zbl 0555.35067Cazenave, Thierry; Lions, Pierre-Louis 78 1984 Comparison results for elliptic and parabolic equations via Schwarz symmetrization. Zbl 0703.35007Alvino, Angelo; Trombetti, Guido; Lions, Pierre-Louis 77 1990 Multi-dimensional travelling-wave solutions of a flame propagation model. Zbl 0711.35066Berestycki, H.; Larrouturou, B.; Lions, P. L. 76 1990 Neumann type boundary conditions for Hamilton-Jacobi equations. Zbl 0599.35025Lions, Pierre-Louis 75 1985 Long time average of mean field games. Zbl 1270.35098Cardaliaguet, Pierre; Lasry, Jean-Michel; Lions, Pierre-Louis; Porretta, Alessio 73 2012 On the Fokker-Planck-Boltzmann equation. Zbl 0671.35068DiPerna, R. J.; Lions, P. L. 70 1988 Diffusive limit for finite velocity Boltzmann kinetic models. Zbl 0896.35109Lions, Pierre Louis; Toscani, Giuseppe 70 1997 Hamilton-Jacobi equations in infinite dimensions. I: Uniqueness of viscosity solutions. Zbl 0627.49013Crandall, Michael G.; Lions, Pierre-Louis 69 1985 Fully nonlinear stochastic partial differential equations: Non-smooth equations and applications. Zbl 0924.35203Lions, Pierre-Louis; Souganidis, Panagiotis E. 66 1998 Quelques remarques sur les problèmes elliptiques quasilinéaires du second ordre. (Some remarks on second order quasilinear elliptic problems). Zbl 0614.35034Lions, P. L. 64 1985 Fully nonlinear stochastic partial differential equations. Zbl 1002.60552Lions, Pierre-Louis; Souganidis, Panagiotis E. 64 1998 Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting. Zbl 1050.35012Lions, Pierre-Louis; Souganidis, Panagiotis E. 64 2003 Homogenization of “viscous” Hamilton–Jacobi equations in stationary ergodic media. Zbl 1065.35047Lions, Pierre-Louis; Souganidis, Panagiotis E. 63 2005 Renormalized solutions of some transport equations with partially \(W^{1,1}\) velocities and applications. Zbl 1170.35364Le Bris, C.; Lions, P.-L. 62 2004 Long time average of mean field games with a nonlocal coupling. Zbl 1332.35364Cardaliaguet, P.; Lasry, J.-M.; Lions, P.-L.; Porretta, A. 62 2013 On Boltzmann and Landau equations. Zbl 0809.35137Lions, P. L. 60 1994 Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. I: The case of bounded stochastic evolutions. Zbl 0757.93082Lions, P. L. 60 1988 On ergodic stochastic control. Zbl 1126.93434Arisawa, M.; Lions, P.-L. 60 1998 Partial differential equation models in macroeconomics. Zbl 1353.91027Achdou, Yves; Buera, Francisco J.; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin 60 2014 The Neumann problem for equations of Monge-Ampère type. Zbl 0604.35027Lions, P.-L.; Trudinger, N. S.; Urbas, J. I. E. 59 1986 From atoms to crystals: a mathematical journey. Zbl 1136.81371Le Bris, Claude; Lions, Pierre-Louis 58 2005 Differential games, optimal control and directional derivatives of viscosity solutions of Bellman’s and Isaacs’ equations. Zbl 0569.49019Lions, Pierre-Louis; Souganidis, P. E. 58 1985 Sobolev imbedding theorems in borderline cases. Zbl 0841.46023Fusco, Nicola; Lions, Pierre Louis; Sbordone, Carlo 57 1996 Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. I: A necessary and sufficient condition for the stability of general molecular systems. Zbl 0767.35065Catto, I.; Lions, P. L. 56 1992 Hamilton-Jacobi equations in infinite dimensions. II: Existence of viscosity solutions. Zbl 0639.49021Crandall, Michael G.; Lions, Pierre-Louis 56 1986 Two remarks on Monge-Ampère equations. Zbl 0594.35023Lions, Pierre-Louis 55 1985 Best constants in Sobolev inequalities for functions vanishing on some part of the boundary and related questions. Zbl 0631.46033Lions, P. L.; Pacella, F.; Tricarico, M. 53 1988 Income and wealth distribution in macroeconomics: a continuous-time approach. Zbl 1484.91177Achdou, Yves; Han, Jiequn; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin 20 2022 A spectral dominance approach to large random matrices. Zbl 1492.60013Bertucci, Charles; Debbah, Mérouane; Lasry, Jean-Michel; Lions, Pierre-Louis 2 2022 Dimension reduction techniques in deterministic mean field games. Zbl 1490.91019Lasry, Jean-Michel; Lions, Pierre-Louis; Seeger, Benjamin 2 2022 A class of short-term models for the oil industry that accounts for speculative oil storage. Zbl 1494.91139Achdou, Yves; Bertucci, Charles; Lasry, Jean-Michel; Lions, Pierre-Louis; Rostand, Antoine; Scheinkman, José A. 1 2022 Master equation for the finite state space planning problem. Zbl 1470.91010Bertucci, Charles; Lasry, Jean-Michel; Lions, Pierre-Louis 4 2021 Optimal control of conditioned processes with feedback controls. Zbl 1459.93188Achdou, Yves; Laurière, Mathieu; Lions, Pierre-Louis 3 2021 Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians. Zbl 1434.60155Gassiat, Paul; Gess, Benjamin; Lions, Pierre-Louis; Souganidis, Panagiotis E. 7 2020 New regularity results for Hamilton-Jacobi equations and long time behavior of pathwise (stochastic) viscosity solutions. Zbl 1444.60065Lions, Pierre-Louis; Souganidis, Panagiotis E. 5 2020 Strategic advantages in mean field games with a major player. (Avantages stratégiques dans des jeux à champ moyen avec un agent majoritaire.) Zbl 1445.91002Bertucci, Charles; Lasry, Jean-Michel; Lions, Pierre-Louis 2 2020 Homogenization of the backward-forward mean-field games systems in periodic environments. Zbl 1467.35036Lions, Pierre-Louis; Souganidis, Panagiotis E. 1 2020 Extended mean-field games. Zbl 1460.35020Lions, Pierre-Louis; Souganidis, Panagiotis E. 1 2020 The asymptotics of stochastically perturbed reaction-diffusion equations and front propagation. Zbl 1453.60122Lions, Pierre-Louis; Souganidis, Panagiotis E. 1 2020 The master equation and the convergence problem in mean field games. Zbl 1430.91002Cardaliaguet, Pierre; Delarue, François; Lasry, Jean-Michel; Lions, Pierre-Louis 114 2019 Some remarks on mean field games. Zbl 1411.91100Bertucci, Charles; Lasry, Jean-Michel; Lions, Pierre-Louis 29 2019 On correctors for linear elliptic homogenization in the presence of local defects: the case of advection-diffusion. Zbl 1416.35092Blanc, X.; Le Bris, Claude; Lions, P.-L. 4 2019 Parabolic equations with irregular data and related issues. Applications to stochastic differential equations. Zbl 07046231Le Bris, Claude; Lions, Pierre-Louis 4 2019 Mean-field games with a major player. (Jeux à champ moyen avec agent dominant.) Zbl 1410.91048Lasry, Jean-Michel; Lions, Pierre-Louis 15 2018 On correctors for linear elliptic homogenization in the presence of local defects. Zbl 1423.35092Blanc, X.; Le Bris, C.; Lions, P.-L. 14 2018 Well-posedness for multi-dimensional junction problems with Kirchoff-type conditions. Zbl 1380.35055Lions, Pierre-Louis; Souganidis, Panagiotis E. 14 2017 Eikonal equations and pathwise solutions to fully non-linear SPDEs. Zbl 1377.35293Friz, Peter K.; Gassiat, Paul; Lions, Pierre-Louis; Souganidis, Panagiotis E. 14 2017 Efficiency of the price formation process in presence of high frequency participants: a mean field game analysis. Zbl 1404.91245Lachapelle, Aimé; Lasry, Jean-Michel; Lehalle, Charles-Albert; Lions, Pierre-Louis 25 2016 The dynamics of inequality. Zbl 1420.91061Gabaix, Xavier; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin 25 2016 Viscosity solutions for junctions: well posedness and stability. Zbl 1353.35111Lions, Pierre-Louis; Souganidis, Panagiotis 23 2016 A long-term mathematical model for mining industries. Zbl 1411.91428Achdou, Yves; Giraud, Pierre-Noel; Lasry, Jean-Michel; Lions, Pierre-Louis 6 2016 Local profiles for elliptic problems at different scales: defects in, and interfaces between periodic structures. Zbl 1333.35003Blanc, X.; Le Bris, C.; Lions, P.-L. 24 2015 Local profiles and elliptic problems at different scales with defects. (Profils locaux et problèmes elliptiques à plusieurs échelles avec défauts.) Zbl 1312.35054Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 6 2015 Partial differential equation models in macroeconomics. Zbl 1353.91027Achdou, Yves; Buera, Francisco J.; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin 60 2014 Scalar conservation laws with rough (stochastic) fluxes: the spatially dependent case. Zbl 1323.35233Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E. 29 2014 Long time average of mean field games with a nonlocal coupling. Zbl 1332.35364Cardaliaguet, P.; Lasry, J.-M.; Lions, P.-L.; Porretta, A. 62 2013 Scalar conservation laws with rough (stochastic) fluxes. Zbl 1333.60140Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E. 37 2013 Stochastic averaging lemmas for kinetic equations. Zbl 1323.35234Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E. 15 2013 Mathematical topics in fluid mechanics. Vol. 2: Compressible models. Reprint of the 1998 hardback ed. Zbl 1264.76003Lions, Pierre-Louis 4 2013 Long time average of mean field games. Zbl 1270.35098Cardaliaguet, Pierre; Lasry, Jean-Michel; Lions, Pierre-Louis; Porretta, Alessio 73 2012 A possible homogenization approach for the numerical simulation of periodic microstructures with defects. Zbl 1255.74051Blanc, X.; Le Bris, C.; Lions, P.-L. 18 2012 From the Newton equation to the wave equation in some simple cases. Zbl 1259.35163Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 1 2012 Mean field games and applications. Zbl 1205.91027Guéant, Olivier; Lasry, Jean-Michel; Lions, Pierre-Louis 122 2011 Stochastic homogenization of Hamilon-Jacobi and “viscous”-Hamilton-Jacobi equations with convex nonlinearities – revisited. Zbl 1197.35031Lions, Pierre-Louis; Souganidis, Panagiotis E. 33 2010 A discussion about the homogenization of moving interfaces. Zbl 1180.35070Cardaliaguet, P.; Lions, P.-L.; Souganidis, P. E. 18 2009 Existence and uniqueness of solutions to Fokker-Planck type equations with irregular coefficients. Zbl 1157.35301Le Bris, C.; Lions, P.-L. 103 2008 Ergodic problems and periodic homogenization for fully nonlinear equations in half-space type domains with Neumann boundary conditions. Zbl 1173.35013Barles, G.; da Lio, F.; Lions, P.-L.; Souganidis, P. E. 18 2008 Molecular simulation and related topics: some open mathematical problems. Zbl 1158.35100Cancès, Eric; Le Bris, C.; Lions, P.-L. 6 2008 Mean field games. Zbl 1156.91321Lasry, Jean-Michel; Lions, Pierre-Louis 833 2007 Correlations and bounds for stochastic volatility models. Zbl 1108.62110Lions, P.-L.; Musiela, M. 39 2007 Global existence of weak solutions to some micro-macro models. Zbl 1117.35312Lions, Pierre-Louis; Masmoudi, Nader 36 2007 Stochastic homogenization and random lattices. Zbl 1129.60055Blanc, X.; Le Bris, C.; Lions, P.-L. 31 2007 The energy of some microscopic stochastic lattices. Zbl 1173.82308Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 31 2007 Atomistic to continuum limits for computational materials science. Zbl 1144.82018Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 21 2007 Large investor trading impacts on volatility. Zbl 1160.91016Lions, Pierre-Louis; Lasry, Jean-Michel 11 2007 Two remarks on generalized flows for ordinary differential equations. (Deux remarques sur les flots généralisés d’équations différentielles ordinaires.) Zbl 1132.34043Hauray, Maxime; Le Bris, Claude; Lions, Pierre-Louis 8 2007 Instantaneous self-fulfilling of long-term prophecies on the probabilistic distribution of financial asset values. Zbl 1130.91340Lions, P.-L.; Lasry, J.-M. 5 2007 Large investor trading impacts on volatility. Zbl 1153.91428Lions, Pierre-Louis; Lasry, Jean-Michel 5 2007 Mean field games. I: The stationary case. (Jeux à champ moyen. I: Le cas stationnaire.) Zbl 1153.91009Lasry, Jean-Michel; Lions, Pierre-Louis 383 2006 Mean field games. II: Finite horizon and optimal control. (Jeux à champ moyen. II: Horizon fini et contrôle optimal.) Zbl 1153.91010Lasry, Jean-Michel; Lions, Pierre-Louis 352 2006 A variant of stochastic homogenization theory for elliptic operators. (Une variante de la théorie de l’homogénéisation stochastique des opérateurs elliptiques.) Zbl 1103.35014Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 20 2006 Convexity of solutions of parabolic equations. Zbl 1096.35006Lions, Pierre-Louis; Musiela, Marek 14 2006 Towards a self-consistent theory of volatility. Zbl 1127.91027Lions, Pierre-Louis; Lasry, Jean-Michel 7 2006 Discrete to continuum limit for some models of stochastic lattices of atoms. (Du discret au continu pour des modèles de réseaux aléatoires d’atomes.) Zbl 1095.74006Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 5 2006 Some properties of diffusion processes with singular coefficients. Zbl 1104.60045Lions, Pierre-Louis; Musiela, Marek 3 2006 Homogenization of “viscous” Hamilton–Jacobi equations in stationary ergodic media. Zbl 1065.35047Lions, Pierre-Louis; Souganidis, Panagiotis E. 63 2005 From atoms to crystals: a mathematical journey. Zbl 1136.81371Le Bris, Claude; Lions, Pierre-Louis 58 2005 Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications. Zbl 1135.35092Lions, Pierre-Louis; Souganidis, Panagiotis E. 43 2005 On the uniqueness of the solution of the two-dimensional Navier–Stokes equation with a Dirac mass as initial vorticity. Zbl 1083.35092Gallagher, Isabelle; Gallay, Thierry; Lions, Pierre-Louis 16 2005 Homogenization of the Euler system in a 2D porous medium. Zbl 1072.35032Lions, P.-L.; Masmoudi, N. 12 2005 Renormalized solutions of some transport equations with partially \(W^{1,1}\) velocities and applications. Zbl 1170.35364Le Bris, C.; Lions, P.-L. 62 2004 Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting. Zbl 1050.35012Lions, Pierre-Louis; Souganidis, Panagiotis E. 64 2003 A definition of the ground state energy for systems composed of infinitely many particles. Zbl 1035.82004Blanc, X.; Le Bris, C.; Lions, P. L. 20 2003 From molecular models to continuum mechanics. Zbl 1028.74005Blanc, X.; Le Bris, C.; Lions, P.-L. 99 2002 On some periodic Hartree-type models for crystals. Zbl 1005.81101Catto, I.; Le Bris, C.; Lions, P.-L. 32 2002 Characterization of functions on \(\mathbb{R}^3\) with bounded Newtonian potential. (Caractérisation des fonctions de \(\mathbb{R}^3\) à potentiel newtonien borné.) Zbl 0995.35028Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 4 2002 From the Boltzmann equations to the equations of incompressible fluid mechanics. I, II. Zbl 0987.76088Lions, P.-L.; Masmoudi, N. 126 2001 Applications of Malliavin calculus to Monte-Carlo methods in finance. II. Zbl 0973.60061Fournié, Eric; Lasry, Jean-Michel; Lebuchoux, Jérôme; Lions, Pierre-Louis 79 2001 On the thermodynamic limit for Hartree-Fock type models. Zbl 0994.35115Catto, I.; Le Bris, C.; Lions, P.-L. 49 2001 Uniqueness of mild solutions of the Navier-Stokes system in \(L^N\). Zbl 1086.35077Lions, P.-L.; Masmoudi, N. 40 2001 A deterministic particle method for nonlinear diffusion equations. (Une méthode particulaire déterministe pour des équations diffusives non linéaires.) Zbl 0973.65003Lions, Pierre-Louis; Mas-Gallic, Sylvie 29 2001 Convergence of molecular models to continuum mechanics models. (Convergence de modèles moléculaires vers des modèles de mécanique des milieux continus.) Zbl 0986.74006Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 10 2001 Global solutions for some Oldroyd models of non-Newtonian flows. Zbl 0957.35109Lions, P. L.; Masmoudi, N. 151 2000 Uniqueness of weak solutions of fully nonlinear stochastic partial differential equations. Zbl 0970.60072Lions, Pierre-Louis; Souganidis, Panagiotis E. 37 2000 Fully nonlinear stochastic PDE with semilinear stochastic dependence. Zbl 0966.60058Lions, Pierre-Louis; Souganidis, Panagiotis E. 36 2000 Equilibrium statistical theory for nearly parallel vortex filaments. Zbl 1041.76038Lions, Pierre-Louis; Majda, Andrew 22 2000 On some challenging problems in nonlinear partial differential equations. Zbl 0972.35094Lions, P.-L. 7 2000 A new class of singular stochastic control problems. (Une classe nouvelle de problèmes singuliers de contrôle stochastique.) Zbl 0971.49015Lasry, Jean-Michel; Lions, Pierre-Louis 6 2000 A characterization of the existence of solutions for Hamilton-Jacobi equations in ergodic control problems with applications. Zbl 0967.35029Arisawa, M.; Ishii, H.; Lions, P.-L. 2 2000 Applications of Malliavin calculus to Monte Carlo methods in finance. Zbl 0947.60066Fournié, Eric; Lasry, Jean-Michel; Lebuchous, Jérôme; Lions, Pierre-Louis 156 1999 Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions. Zbl 0992.35067Desjardins, B.; Grenier, E.; Lions, P.-L.; Masmoudi, N. 93 1999 A local approach to the incompressible limit. (Une approche locale de la limite incompressible.) Zbl 0937.35132Lions, Pierre-Louis; Masmoudi, Nader 45 1999 Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations. Zbl 0927.35029Crandall, M. G.; Kocan, M.; Lions, P. L.; Świȩch, A. 41 1999 On a free boundary barotropic model. Zbl 0917.76073Lions, P.-L.; Masmoudi, N. 25 1999 Bounds on the density for compressible isentropic Navier-Stokes equations with Dirichlet boundary conditions. (Bornes sur la densité pour les équations de Navier-Stokes compressibles isentropiques avec conditions aux limites de Dirichlet.) Zbl 0931.35126Lions, Pierre-Louis 15 1999 Comparison results for solutions of elliptic problems via symmetrization. Zbl 0924.35038Alvino, Angelo; Trombetti, Guido; Lions, Pierre-Louis; Matarasso, Silvano 13 1999 Stochastic control under partial information and applications to finance. (Contrôle stochastique avec informations partielles et applications à la finance.) Zbl 0937.93058Laskry, Jean-Michel; Lions, Pierre-Louis 8 1999 Nonlinear stochastic partial differential equations and viscosity solutions. (Équations aux dérivées partielles stochastiques nonlinéaires et solutions de viscosité.) Zbl 1061.35530Lions, P.-L.; Souganidis, P. E. 6 1999 Mathematical topics in fluid mechanics. Vol. 2: Compressible models. Zbl 0908.76004Lions, Pierre-Louis 523 1998 Incompressible limit for a viscous compressible fluid. Zbl 0909.35101Lions, P.-L.; Masmoudi, N. 199 1998 Fully nonlinear stochastic partial differential equations: Non-smooth equations and applications. Zbl 0924.35203Lions, Pierre-Louis; Souganidis, Panagiotis E. 66 1998 Fully nonlinear stochastic partial differential equations. Zbl 1002.60552Lions, Pierre-Louis; Souganidis, Panagiotis E. 64 1998 On ergodic stochastic control. Zbl 1126.93434Arisawa, M.; Lions, P.-L. 60 1998 The mathematical theory of thermodynamic limits: Thomas-Fermi type models. Zbl 0938.81001Catto, Isabelle; Le Bris, Claude; Lions, Pierre-Louis 40 1998 Regularity and compactness for Boltzmann collision kernels without angular cut-off. (Régularité et compacité pour des noyaux de collision de Boltzmann sans troncature angulaire.) Zbl 0920.35114Lions, Pierre-Louis 28 1998 On ordinary differential equations and transport equations. (Sur les équations différentielles ordinaires et les équations de transport.) Zbl 0919.34028Lions, Pierre-Louis 21 1998 Identification of the dual cone of convex functions and applications. (Identification du cône dual des fonctions convexes et applications.) Zbl 0924.46059Lions, Pierre-Louis 11 1998 ...and 258 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 13,556 Authors 143 Lions, Pierre-Louis 96 Alves, Claudianor Oliveira 88 Tang, Xianhua 82 Feireisl, Eduard 71 Perthame, Benoît 70 Souganidis, Panagiotis E. 65 Tang, Chun-Lei 59 Cardaliaguet, Pierre 57 Do Ó, João M. Bezerra 55 Rossi, Julio Daniel 54 Ishii, Hitoshi 53 Wang, Zhi-Qiang 52 Barles, Guy 52 Figueiredo, Giovany Malcher 52 Masmoudi, Nader 51 Zou, Wenming 49 Miyagaki, Olimpio Hiroshi 47 Wu, Tsungfang 47 Yang, Minbo 46 Gomes, Diogo Luís Aguiar 46 Wei, Juncheng 44 Le Bris, Claude 42 Osher, Stanley Joel 40 Squassina, Marco 39 Nečasová, Šárka 39 Novotný, Antonín 38 Chen, Haibo 38 Ding, Yanheng 38 Wang, Jun 38 Winkler, Michael 37 Porretta, Alessio 36 Ambrosio, Vincenzo 36 Yang, Jianfu 36 Zhang, Jian 36 Zhang, Xianwen 35 Cannarsa, Piermarco 35 Rădulescu, Vicenţiu D. 34 Cianchi, Andrea 34 Crippa, Gianluca 34 Giga, Yoshikazu 34 Golse, François 34 Lu, Guozhen 34 Quaas, Alexander 34 Wang, Dehua 34 Zhang, Jianjun 33 Bayraktar, Erhan 33 Chen, Gui-Qiang G. 33 Chen, Sitong 33 Zhang, Ping 32 Lewin, Mathieu 32 Li, Juan 32 Peng, Shuangjie 31 Ambrosio, Luigi 31 Cao, Daomin 31 Jeanjean, Louis 31 Pucci, Patrizia 31 Świȩch, Andrzej 31 Vasseur, Alexis F. 30 Camilli, Fabio 30 Markowich, Peter Alexander 29 Chen, Jianqing 29 Kang, Dongsheng 29 Kwon, Young-Sam 28 Buckdahn, Rainer 28 Capuzzo Dolcetta, Italo 28 Carrillo de la Plata, José Antonio 28 Felmer, Patricio L. 28 Flandoli, Franco 28 Jin, Shi 28 Li, Gongbao 28 Liang, Sihua 28 Mitake, Hiroyoshi 28 Monneau, Régis 28 Tran Vinh Hung 28 Van Schaftingen, Jean 28 Vazquez, Juan Luis 28 Yang, Tong 27 Bartolucci, Daniele 27 Benci, Vieri 27 Berestycki, Henri 27 Goudon, Thierry 27 Jabin, Pierre-Emmanuel 27 Saanouni, Tarek 27 Touzi, Nizar 27 Yang, Dachun 27 Zhang, Binlin 27 Zhong, Xin 26 Byeon, Jaeyoung 26 Cholamjiak, Prasit 26 Deng, Yinbin 26 Desvillettes, Laurent 26 Esteban, Maria J. 26 Frankowska, Hélène 26 Karlsen, Kenneth Hvistendahl 25 Cirant, Marco 25 Hsu, TsingSan 25 Huang, Feimin 25 Novaga, Matteo 25 Ruf, Bernhard 25 Soner, Halil Mete ...and 13,456 more Authors all top 5 Cited in 758 Serials 994 Journal of Differential Equations 800 Journal of Mathematical Analysis and Applications 791 Nonlinear Analysis. 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(English Edition) 54 Journal of Dynamics and Differential Equations 52 Computer Methods in Applied Mechanics and Engineering 51 Acta Mathematicae Applicatae Sinica. English Series 49 Journal of Inequalities and Applications 48 Duke Mathematical Journal 48 Mathematische Nachrichten 48 Chinese Annals of Mathematics. Series B 48 SIAM Journal on Optimization 47 Journal of Hyperbolic Differential Equations 47 Journal of Fixed Point Theory and Applications 46 Quarterly of Applied Mathematics 46 Topological Methods in Nonlinear Analysis 43 Computational Optimization and Applications 43 Journal of the European Mathematical Society (JEMS) 43 Discrete and Continuous Dynamical Systems. Series S 42 Systems & Control Letters 42 Stochastic Analysis and Applications 41 SIAM Journal on Numerical Analysis 40 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 40 Fixed Point Theory and Applications 39 Journal of Nonlinear Science 39 SN Partial Differential Equations and Applications 38 Journal d’Analyse Mathématique 37 Mathematics of Operations Research ...and 658 more Serials all top 5 Cited in 60 Fields 12,540 Partial differential equations (35-XX) 2,797 Calculus of variations and optimal control; optimization (49-XX) 2,539 Fluid mechanics (76-XX) 2,127 Numerical analysis (65-XX) 1,755 Probability theory and stochastic processes (60-XX) 1,428 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1,268 Operator theory (47-XX) 1,099 Statistical mechanics, structure of matter (82-XX) 974 Systems theory; control (93-XX) 840 Operations research, mathematical programming (90-XX) 730 Global analysis, analysis on manifolds (58-XX) 729 Functional analysis (46-XX) 572 Information and communication theory, circuits (94-XX) 543 Ordinary differential equations (34-XX) 511 Quantum theory (81-XX) 492 Dynamical systems and ergodic theory (37-XX) 492 Computer science (68-XX) 441 Biology and other natural sciences (92-XX) 395 Differential geometry (53-XX) 394 Real functions (26-XX) 372 Mechanics of deformable solids (74-XX) 267 Harmonic analysis on Euclidean spaces (42-XX) 252 Optics, electromagnetic theory (78-XX) 239 Integral equations (45-XX) 212 Mechanics of particles and systems (70-XX) 163 Classical thermodynamics, heat transfer (80-XX) 118 Statistics (62-XX) 107 Potential theory (31-XX) 92 Relativity and gravitational theory (83-XX) 91 Astronomy and astrophysics (85-XX) 78 Geophysics (86-XX) 76 Convex and discrete geometry (52-XX) 74 Measure and integration (28-XX) 63 Several complex variables and analytic spaces (32-XX) 56 Functions of a complex variable (30-XX) 55 Approximations and expansions (41-XX) 53 Difference and functional equations (39-XX) 38 General topology (54-XX) 36 Linear and multilinear algebra; matrix theory (15-XX) 33 General and overarching topics; collections (00-XX) 27 Abstract harmonic analysis (43-XX) 22 Topological groups, Lie groups (22-XX) 20 Combinatorics (05-XX) 19 History and biography (01-XX) 18 Algebraic topology (55-XX) 18 Manifolds and cell complexes (57-XX) 14 Integral transforms, operational calculus (44-XX) 13 Special functions (33-XX) 9 Mathematical logic and foundations (03-XX) 8 Algebraic geometry (14-XX) 7 Geometry (51-XX) 5 Nonassociative rings and algebras (17-XX) 5 Group theory and generalizations (20-XX) 3 Number theory (11-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Sequences, series, summability (40-XX) 2 Mathematics education (97-XX) 1 General algebraic systems (08-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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