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 Videos: carmin.tv Awards: Fields Medal (1994) Documents Indexed: 392 Publications since 1977, including 9 Books and 10 Additional arXiv Preprints 7 Contributions as Editor · 1 Further Contribution Reviewing Activity: 1 Review Biographic References: 4 Publications Co-Authors: 115 Co-Authors with 277 Joint Publications 4,264 Co-Co-Authors all top 5 Co-Authors 117 single-authored 40 Souganidis, Panagiotis E. 39 Lasry, Jean-Michel 27 Le Bris, Claude 22 Crandall, Michael G. 15 Blanc, Xavier 14 Perthame, Benoît 12 Berestycki, Henri 12 Bertucci, Charles 12 Catto, Isabelle 11 DiPerna, Ronald J. 10 Alvino, Angelo 10 Masmoudi, Nader 10 Trombetti, Guido 7 Achdou, Yves 6 Esteban, Maria J. 6 Morel, Jean-Michel 5 Bahri, Abbas 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 4 Seeger, Benjamin 3 Coifman, Ronald Raphaël 3 Guedes de Figueiredo, Djairo 3 Díaz Díaz, Jesús Ildefonso 3 Fournié, Eric 3 Gassiat, Paul 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 Gess, Benjamin 2 Gogny, D. 2 Laurière, Mathieu 2 Marchioro, Carlo 2 Nussbaum, Roger David 2 Pacella, Filomena 2 Porretta, Alessio 2 Pulvirenti, Mario 2 Rostand, Antoine 2 Scheinkman, José Alexandre 2 Sznitman, Alain-Sol 2 Toscani, Giuseppe 2 Urbas, John Ivan Eugene 1 Alziary, Bénédicte 1 Bensoussan, Alain 1 Bertozzi, Andrea Louise 1 Bertucci, Louis 1 Buera, Francisco J. 1 Caflisch, Russ 1 Cancès, Eric 1 Carmona, René A. 1 Catté, Francine 1 Chambolle, Antonin 1 Chan, Tony Fan-Cheong 1 Chen, Nan 1 Coll, Tomeu 1 Constantin, Peter 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 E, Weinan 1 Ekeland, Ivar 1 Engquist, Bjorn E. 1 Fefferman, Charles Louis 1 Ferone, Vincenzo 1 Fleming, Wendell Helms 1 Friedman, Avner 1 Friz, Peter 1 Fusco, Nicola 1 Gabaix, Xavier 1 Gallagher, Isabelle 1 Gallay, Thierry 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 Keller, Gerta 1 Khouider, Boualem 1 Klein, Rupert ...and 37 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 13 Journal of Functional Analysis 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 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 Illinois Journal of Mathematics 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 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 Notices of the American Mathematical Society 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 SIAM Journal on Financial Mathematics 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 ...and 1 more Serials all top 5 Fields 279 Partial differential equations (35-XX) 98 Calculus of variations and optimal control; optimization (49-XX) 63 Fluid mechanics (76-XX) 51 Probability theory and stochastic processes (60-XX) 40 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 40 Systems theory; control (93-XX) 33 Statistical mechanics, structure of matter (82-XX) 28 Functional analysis (46-XX) 25 Operator theory (47-XX) 24 Numerical analysis (65-XX) 24 Quantum theory (81-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 History and biography (01-XX) 2 Real functions (26-XX) 2 Convex and discrete geometry (52-XX) 2 Differential geometry (53-XX) 2 Algebraic topology (55-XX) 2 Geophysics (86-XX) 1 Difference and functional equations (39-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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 367 Publications have been cited 34,217 times in 21,649 Documents Cited by ▼ Year ▼ User’s guide to viscosity solutions of second order partial differential equations. Zbl 0755.35015 Crandall, Michael G.; Ishii, Hitoshi; Lions, Pierre-Louis 2,239 1992 Nonlinear scalar field equations. I: Existence of a ground state. Zbl 0533.35029 Berestycki, Henri; Lions, Pierre-Louis 1,535 1983 The concentration-compactness principle in the calculus of variations. The locally compact case. I. Zbl 0541.49009 Lions, Pierre-Louis 1,261 1984 The concentration-compactness principle in the calculus of variations. The locally compact case. II. Zbl 0704.49004 Lions, P.-L. 1,177 1984 Mathematical topics in fluid mechanics. Vol. 1: Incompressible models. Zbl 0866.76002 Lions, Pierre-Louis 1,102 1996 Mean field games. Zbl 1156.91321 Lasry, Jean-Michel; Lions, Pierre-Louis 1,084 2007 The concentration-compactness principle in the calculus of variations. The limit case. I. Zbl 0704.49005 Lions, P.-L. 1,058 1985 Ordinary differential equations, transport theory and Sobolev spaces. Zbl 0696.34049 DiPerna, R. J.; Lions, P. L. 1,024 1989 Mathematical topics in fluid mechanics. Vol. 2: Compressible models. Zbl 0908.76004 Lions, Pierre-Louis 1,020 1998 Viscosity solutions of Hamilton-Jacobi equations. Zbl 0599.35024 Crandall, Michael G.; Lions, Pierre-Louis 1,017 1983 Splitting algorithms for the sum of two nonlinear operators. Zbl 0426.65050 Lions, Pierre-Louis; Mercier, B. 878 1979 On the Cauchy problem for Boltzmann equations: Global existence and weak stability. Zbl 0698.45010 DiPerna, R. J.; Lions, P. L. 650 1989 Orbital stability of standing waves for some nonlinear Schrödinger equations. Zbl 0513.35007 Cazenave, T.; Lions, Pierre-Louis 581 1982 The concentration-compactness principle in the calculus of variations. The limit case. II. Zbl 0704.49006 Lions, P.-L. 531 1985 Generalized solutions of Hamilton-Jacobi equations. Zbl 0497.35001 Lions, Pierre-Louis 480 1982 Mean field games. I: The stationary case. (Jeux à champ moyen. I: Le cas stationnaire.) Zbl 1153.91009 Lasry, Jean-Michel; Lions, Pierre-Louis 461 2006 Image recovery via total variation minimization and related problems. Zbl 0874.68299 Chambolle, Antonin; Lions, Pierre-Louis 453 1997 Some properties of viscosity solutions of Hamilton-Jacobi equations. Zbl 0543.35011 Crandall, M. G.; Evans, L. C.; Lions, Pierre-Louis 448 1984 Nonlinear scalar field equations. II: Existence of infinitely many solutions. Zbl 0556.35046 Berestycki, Henri; Lions, Pierre-Louis 429 1983 Mean field games. II: Finite horizon and optimal control. (Jeux à champ moyen. II: Horizon fini et contrôle optimal.) Zbl 1153.91010 Lasry, Jean-Michel; Lions, Pierre-Louis 428 2006 The Choquard equation and related questions. Zbl 0453.47042 Lions, Pierre-Louis 426 1980 Compensated compactness and Hardy spaces. Zbl 0864.42009 Coifman, R.; Lions, P. L.; Meyer, Y.; Semmes, S. 417 1993 Stochastic differential equations with reflecting boundary conditions. Zbl 0598.60060 Lions, Pierre-Louis; Sznitman, A. S. 370 1984 On the existence of positive solutions of semilinear elliptic equations. Zbl 0511.35033 Lions, Pierre-Louis 343 1982 Solutions of Hartree-Fock equations for Coulomb systems. Zbl 0618.35111 Lions, P. L. 338 1987 Propagation of moments and regularity for the 3-dimensional Vlasov- Poisson system. Zbl 0741.35061 Lions, P. L.; Perthame, B. 280 1991 Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. Zbl 0708.35031 Ishii, H.; Lions, P. L. 278 1990 Symétrie et compacité dans les espaces de Sobolev. Zbl 0501.46032 Lions, Pierre-Louis 266 1982 Image selective smoothing and edge detection by nonlinear diffusion. Zbl 0746.65091 Catté, Francine; Lions, Pierre-Louis; Morel, Jean-Michel; Coll, Tomeu 265 1992 On Wigner measures. (Sur les mesures de Wigner.) Zbl 0801.35117 Lions, Pierre Louis; Paul, Thierry 258 1993 On the Schwarz alternating method. I. Zbl 0658.65090 Lions, P. L. 252 1988 A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description. Zbl 0745.76001 Caglioti, E.; Lions, P. L.; Marchioro, C.; Pulvirenti, M. 245 1992 A priori estimates and existence of positive solutions of semilinear elliptic equations. Zbl 0452.35030 de Figueiredo, D. G.; Lions, Pierre-Louis; Nussbaum, R. D. 243 1982 A kinetic formulation of multidimensional scalar conservation laws and related equations. Zbl 0820.35094 Lions, P. L.; Perthame, B.; Tadmor, E. 237 1994 Incompressible limit for a viscous compressible fluid. Zbl 0909.35101 Lions, P.-L.; Masmoudi, N. 222 1998 Regularity of the moments of the solution of a transport equation. Zbl 0652.47031 Golse, François; Lions, Pierre-Louis; Perthame, Benoît; Sentis, Rémi 221 1988 Two approximations of solutions of Hamilton-Jacobi equations. Zbl 0556.65076 Crandall, M. G.; Lions, Pierre-Louis 207 1984 Mean field games and applications. Zbl 1205.91027 Guéant, Olivier; Lasry, Jean-Michel; Lions, Pierre-Louis 206 2011 Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. II: Viscosity solutions and uniqueness. Zbl 0716.49023 Lions, P.-L. 203 1983 The master equation and the convergence problem in mean field games. Zbl 1430.91002 Cardaliaguet, Pierre; Delarue, François; Lasry, Jean-Michel; Lions, Pierre-Louis 202 2019 Approximation de points fixes de contractions. Zbl 0349.47046 Lions, Pierre-Louis 198 1977 On the Schwarz alternating method. III: A variant for nonoverlapping subdomains. Zbl 0704.65090 Lions, P. L. 192 1990 Kinetic formulation of the isentropic gas dynamics and \(p\)-systems. Zbl 0799.35151 Lions, P. L.; Perthame, B.; Tadmor, E. 182 1994 Global weak solutions of Vlasov-Maxwell systems. Zbl 0698.35128 DiPerna, R. J.; Lions, P. L. 182 1989 Image selective smoothing and edge detection by nonlinear diffusion. II. Zbl 0766.65117 Alvarez, Luis; Lions, Pierre-Louis; Morel, Jean-Michel 182 1992 Global solutions for some Oldroyd models of non-Newtonian flows. Zbl 0957.35109 Lions, P. L.; Masmoudi, N. 181 2000 Axioms and fundamental equations of image processing. Zbl 0788.68153 Alvarez, Luis; Guichard, Frédéric; Lions, Pierre-Louis; Morel, Jean- Michel 173 1993 Applications of Malliavin calculus to Monte Carlo methods in finance. Zbl 0947.60066 Fournié, Eric; Lasry, Jean-Michel; Lebuchous, Jérôme; Lions, Pierre-Louis 171 1999 Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates. Zbl 0853.76077 Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E. 171 1996 On the existence of a positive solution of semilinear elliptic equations in unbounded domains. Zbl 0883.35045 Bahri, Abbas; Lions, Pierre-Louis 169 1997 Existence and non-existence results for semilinear elliptic problems in unbounded domains. Zbl 0506.35035 Esteban, M. J.; Lions, Pierre-Louis 165 1982 A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description. II. Zbl 0840.76002 Caglioti, E.; Lions, P. L.; Marchioro, C.; Pulvirenti, M. 163 1995 Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints. I: The model problem. Zbl 0688.49026 Lasry, J. M.; Lions, P. L. 162 1989 Produits infinis de resolvantes. Zbl 0387.47038 Brézis, Haïm; Lions, Pierre-Louis 158 1978 An ODE approach to the existence of positive solutions for semilinear problems in \(R^ n\). Zbl 0522.35036 Berestycki, Henri; Lions, Pierre-Louis; Peletier, L. A. 152 1981 From the Boltzmann equations to the equations of incompressible fluid mechanics. I, II. Zbl 0987.76088 Lions, P.-L.; Masmoudi, N. 133 2001 A remark on regularization in Hilbert spaces. Zbl 0631.49018 Lasry, J. M.; Lions, P. L. 120 1986 Convex symmetrization and applications. Zbl 0877.35040 Alvino, Angelo; Ferone, Vincenzo; Trombetti, Guido; Lions, Pierre-Louis 120 1997 Morse index of some min-max critical points. I: Application to multiplicity results. Zbl 0645.58013 Bahri, A.; Lions, P. L. 115 1988 On optimization problems with prescribed rearrangements. Zbl 0678.49003 Alvino, Angelo; Trombetti, Guido; Lions, Pierre-Louis 112 1989 Résolution de problèmes elliptiques quasilineaires. Zbl 0449.35036 Lions, Pierre-Louis 111 1980 Existence and uniqueness of solutions to Fokker-Planck type equations with irregular coefficients. Zbl 1157.35301 Le Bris, C.; Lions, P.-L. 111 2008 Solutions of superlinear elliptic equations and their Morse indices. Zbl 0801.35026 Bahri, A.; Lions, P. L. 110 1992 Hamilton-Jacobi equations with state constraints. Zbl 0702.49019 Capuzzo-Dolcetta, I.; Lions, Pierre-Louis 108 1990 Stationary solutions of nonlinear Schrödinger equations with an external magnetic field. Zbl 0702.35067 Esteban, Maria J.; Lions, Pierre-Louis 107 1989 Asymptotic behavior of some nonlinear heat equations. Zbl 1194.35459 Lions, P. L. 107 1982 Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions. Zbl 0992.35067 Desjardins, B.; Grenier, E.; Lions, P.-L.; Masmoudi, N. 106 1999 From molecular models to continuum mechanics. Zbl 1028.74005 Blanc, X.; Le Bris, C.; Lions, P.-L. 103 2002 Compactness in Boltzmann’s equation via Fourier integral operators and applications. I, II. Zbl 0831.35139 Lions, P. L. 102 1994 \(L^ p\) regularity of velocity averages. Zbl 0763.35014 DiPerna, R. J.; Lions, P. L.; Meyer, Y. 98 1991 Convex viscosity solutions and state constraints. Zbl 0890.49013 Alvarez, O.; Lasry, J.-M.; Lions, P.-L. 96 1997 Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. I: The dynamic programming principle and applications. Zbl 0716.49022 Lions, P.-L. 94 1983 Isolated singularities in semilinear problems. Zbl 0458.35033 Lions, Pierre-Louis 90 1980 On the Schwarz alternating method. II: Stochastic interpretation and order properties. Zbl 0681.65072 Lions, P. L. 89 1989 Comparison results for elliptic and parabolic equations via Schwarz symmetrization. Zbl 0703.35007 Alvino, Angelo; Trombetti, Guido; Lions, Pierre-Louis 87 1990 Long time average of mean field games. Zbl 1270.35098 Cardaliaguet, Pierre; Lasry, Jean-Michel; Lions, Pierre-Louis; Porretta, Alessio 85 2012 Solutions globales d’équations de la chaleur semi linéaires. (Global solutions of semi-linear heat equations). Zbl 0555.35067 Cazenave, Thierry; Lions, Pierre-Louis 83 1984 Neumann type boundary conditions for Hamilton-Jacobi equations. Zbl 0599.35025 Lions, Pierre-Louis 83 1985 Applications of Malliavin calculus to Monte-Carlo methods in finance. II. Zbl 0973.60061 Fournié, Eric; Lasry, Jean-Michel; Lebuchoux, Jérôme; Lions, Pierre-Louis 81 2001 On the Fokker-Planck-Boltzmann equation. Zbl 0671.35068 DiPerna, R. J.; Lions, P. L. 81 1988 Hamilton-Jacobi equations in infinite dimensions. I: Uniqueness of viscosity solutions. Zbl 0627.49013 Crandall, Michael G.; Lions, Pierre-Louis 79 1985 Multi-dimensional travelling-wave solutions of a flame propagation model. Zbl 0711.35066 Berestycki, H.; Larrouturou, B.; Lions, P. L. 79 1990 Diffusive limit for finite velocity Boltzmann kinetic models. Zbl 0896.35109 Lions, Pierre Louis; Toscani, Giuseppe 77 1997 Partial differential equation models in macroeconomics. Zbl 1353.91027 Achdou, Yves; Buera, Francisco J.; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin 76 2014 Fully nonlinear stochastic partial differential equations: Non-smooth equations and applications. Zbl 0924.35203 Lions, Pierre-Louis; Souganidis, Panagiotis E. 75 1998 Quelques remarques sur les problèmes elliptiques quasilinéaires du second ordre. (Some remarks on second order quasilinear elliptic problems). Zbl 0614.35034 Lions, P. L. 74 1985 Fully nonlinear stochastic partial differential equations. Zbl 1002.60552 Lions, Pierre-Louis; Souganidis, Panagiotis E. 73 1998 Long time average of mean field games with a nonlocal coupling. Zbl 1332.35364 Cardaliaguet, P.; Lasry, J.-M.; Lions, P.-L.; Porretta, A. 73 2013 On Boltzmann and Landau equations. Zbl 0809.35137 Lions, P. L. 70 1994 Homogenization of “viscous” Hamilton–Jacobi equations in stationary ergodic media. Zbl 1065.35047 Lions, Pierre-Louis; Souganidis, Panagiotis E. 67 2005 Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. I: The case of bounded stochastic evolutions. Zbl 0757.93082 Lions, P. L. 67 1988 Renormalized solutions of some transport equations with partially \(W^{1,1}\) velocities and applications. Zbl 1170.35364 Le Bris, C.; Lions, P.-L. 66 2004 Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting. Zbl 1050.35012 Lions, Pierre-Louis; Souganidis, Panagiotis E. 66 2003 On ergodic stochastic control. Zbl 1126.93434 Arisawa, M.; Lions, P.-L. 66 1998 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 0767.35065 Catto, I.; Lions, P. L. 66 1992 Hamilton-Jacobi equations in infinite dimensions. II: Existence of viscosity solutions. Zbl 0639.49021 Crandall, Michael G.; Lions, Pierre-Louis 65 1986 From atoms to crystals: a mathematical journey. Zbl 1136.81371 Le Bris, Claude; Lions, Pierre-Louis 65 2005 Two remarks on Monge-Ampère equations. Zbl 0594.35023 Lions, Pierre-Louis 63 1985 The Neumann problem for equations of Monge-Ampère type. Zbl 0604.35027 Lions, P.-L.; Trudinger, N. S.; Urbas, J. I. E. 63 1986 Differential games, optimal control and directional derivatives of viscosity solutions of Bellman’s and Isaacs’ equations. Zbl 0569.49019 Lions, Pierre-Louis; Souganidis, P. E. 62 1985 Long-time behavior of stochastic Hamilton-Jacobi equations. Zbl 1532.35055 Gassiat, Paul; Gess, Benjamin; Lions, Pierre-Louis; Souganidis, Panagiotis E. 1 2024 On Lipschitz solutions of mean field games master equations. Zbl 1544.91043 Bertucci, Charles; Lasry, Jean-Michel; Lions, Pierre-Louis 1 2024 Income and wealth distribution in macroeconomics: a continuous-time approach. Zbl 1484.91177 Achdou, Yves; Han, Jiequn; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin 43 2022 A spectral dominance approach to large random matrices. Zbl 1492.60013 Bertucci, Charles; Debbah, Mérouane; Lasry, Jean-Michel; Lions, Pierre-Louis 4 2022 Interpolation results for pathwise Hamilton-Jacobi equations. Zbl 1501.35131 Lions, Pierre-Louis; Seeger, Benjamin; Souganidis, Panagiotis 3 2022 Dimension reduction techniques in deterministic mean field games. Zbl 1490.91019 Lasry, Jean-Michel; Lions, Pierre-Louis; Seeger, Benjamin 3 2022 A class of short-term models for the oil industry that accounts for speculative oil storage. Zbl 1494.91139 Achdou, Yves; Bertucci, Charles; Lasry, Jean-Michel; Lions, Pierre-Louis; Rostand, Antoine; Scheinkman, José A. 2 2022 Master equation for the finite state space planning problem. Zbl 1470.91010 Bertucci, Charles; Lasry, Jean-Michel; Lions, Pierre-Louis 9 2021 Optimal control of conditioned processes with feedback controls. Zbl 1459.93188 Achdou, Yves; Laurière, Mathieu; Lions, Pierre-Louis 6 2021 Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians. Zbl 1434.60155 Gassiat, Paul; Gess, Benjamin; Lions, Pierre-Louis; Souganidis, Panagiotis E. 9 2020 New regularity results for Hamilton-Jacobi equations and long time behavior of pathwise (stochastic) viscosity solutions. Zbl 1444.60065 Lions, Pierre-Louis; Souganidis, Panagiotis E. 8 2020 Extended mean-field games. Zbl 1460.35020 Lions, Pierre-Louis; Souganidis, Panagiotis E. 7 2020 Strategic advantages in mean field games with a major player. (Avantages stratégiques dans des jeux à champ moyen avec un agent majoritaire.) Zbl 1445.91002 Bertucci, Charles; Lasry, Jean-Michel; Lions, Pierre-Louis 4 2020 The asymptotics of stochastically perturbed reaction-diffusion equations and front propagation. Zbl 1453.60122 Lions, Pierre-Louis; Souganidis, Panagiotis E. 3 2020 Effective transmission conditions for second-order elliptic equations on networks in the limit of thin domains. Zbl 1455.35067 Lions, Pierre-Louis; Souganidis, Panagiotis E. 1 2020 Homogenization of the backward-forward mean-field games systems in periodic environments. Zbl 1467.35036 Lions, Pierre-Louis; Souganidis, Panagiotis E. 1 2020 The master equation and the convergence problem in mean field games. Zbl 1430.91002 Cardaliaguet, Pierre; Delarue, François; Lasry, Jean-Michel; Lions, Pierre-Louis 202 2019 Some remarks on mean field games. Zbl 1411.91100 Bertucci, Charles; Lasry, Jean-Michel; Lions, Pierre-Louis 41 2019 Parabolic equations with irregular data and related issues. Applications to stochastic differential equations. Zbl 07046231 Le Bris, Claude; Lions, Pierre-Louis 10 2019 On correctors for linear elliptic homogenization in the presence of local defects: the case of advection-diffusion. Zbl 1416.35092 Blanc, X.; Le Bris, Claude; Lions, P.-L. 6 2019 On correctors for linear elliptic homogenization in the presence of local defects. Zbl 1423.35092 Blanc, X.; Le Bris, C.; Lions, P.-L. 18 2018 Mean-field games with a major player. (Jeux à champ moyen avec agent dominant.) Zbl 1410.91048 Lasry, Jean-Michel; Lions, Pierre-Louis 18 2018 Scalar conservation laws: initial and boundary value problems revisited and saturated solutions. (Lois de conservation scalaires : retour sur LES problèmes aux limites et solutions saturées.) Zbl 1404.35285 Lions, Pierre-Louis; Souganidis, Panagiotis 1 2018 Well-posedness for multi-dimensional junction problems with Kirchoff-type conditions. Zbl 1380.35055 Lions, Pierre-Louis; Souganidis, Panagiotis E. 25 2017 Eikonal equations and pathwise solutions to fully non-linear SPDEs. Zbl 1377.35293 Friz, Peter K.; Gassiat, Paul; Lions, Pierre-Louis; Souganidis, Panagiotis E. 15 2017 The dynamics of inequality. Zbl 1420.91061 Gabaix, Xavier; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin 46 2016 Viscosity solutions for junctions: well posedness and stability. Zbl 1353.35111 Lions, Pierre-Louis; Souganidis, Panagiotis 32 2016 Efficiency of the price formation process in presence of high frequency participants: a mean field game analysis. Zbl 1404.91245 Lachapelle, Aimé; Lasry, Jean-Michel; Lehalle, Charles-Albert; Lions, Pierre-Louis 30 2016 A long-term mathematical model for mining industries. Zbl 1411.91428 Achdou, Yves; Giraud, Pierre-Noel; Lasry, Jean-Michel; Lions, Pierre-Louis 7 2016 Local profiles for elliptic problems at different scales: defects in, and interfaces between periodic structures. Zbl 1333.35003 Blanc, X.; Le Bris, C.; Lions, P.-L. 30 2015 Local profiles and elliptic problems at different scales with defects. (Profils locaux et problèmes elliptiques à plusieurs échelles avec défauts.) Zbl 1312.35054 Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 6 2015 Partial differential equation models in macroeconomics. Zbl 1353.91027 Achdou, Yves; Buera, Francisco J.; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin 76 2014 Scalar conservation laws with rough (stochastic) fluxes: the spatially dependent case. Zbl 1323.35233 Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E. 34 2014 Long time average of mean field games with a nonlocal coupling. Zbl 1332.35364 Cardaliaguet, P.; Lasry, J.-M.; Lions, P.-L.; Porretta, A. 73 2013 Scalar conservation laws with rough (stochastic) fluxes. Zbl 1333.60140 Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E. 44 2013 Stochastic averaging lemmas for kinetic equations. Zbl 1323.35234 Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E. 19 2013 Mathematical topics in fluid mechanics. Vol. 2: Compressible models. Reprint of the 1998 hardback ed. Zbl 1264.76003 Lions, Pierre-Louis 5 2013 Mathematical topics in fluid mechanics. Volume 1: Incompressible models. Reprint of the 1996 hardback ed. Zbl 1264.76002 Lions, Pierre-Louis 3 2013 Long time average of mean field games. Zbl 1270.35098 Cardaliaguet, Pierre; Lasry, Jean-Michel; Lions, Pierre-Louis; Porretta, Alessio 85 2012 A possible homogenization approach for the numerical simulation of periodic microstructures with defects. Zbl 1255.74051 Blanc, X.; Le Bris, C.; Lions, P.-L. 22 2012 From the Newton equation to the wave equation in some simple cases. Zbl 1259.35163 Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 1 2012 Mean field games and applications. Zbl 1205.91027 Guéant, Olivier; Lasry, Jean-Michel; Lions, Pierre-Louis 206 2011 Stochastic homogenization of Hamilon-Jacobi and “viscous”-Hamilton-Jacobi equations with convex nonlinearities – revisited. Zbl 1197.35031 Lions, Pierre-Louis; Souganidis, Panagiotis E. 33 2010 A discussion about the homogenization of moving interfaces. Zbl 1180.35070 Cardaliaguet, P.; Lions, P.-L.; Souganidis, P. E. 22 2009 Existence and uniqueness of solutions to Fokker-Planck type equations with irregular coefficients. Zbl 1157.35301 Le Bris, C.; Lions, P.-L. 111 2008 Ergodic problems and periodic homogenization for fully nonlinear equations in half-space type domains with Neumann boundary conditions. Zbl 1173.35013 Barles, G.; da Lio, F.; Lions, P.-L.; Souganidis, P. E. 18 2008 Molecular simulation and related topics: some open mathematical problems. Zbl 1158.35100 Cancès, Eric; Le Bris, C.; Lions, P.-L. 8 2008 Mean field games. Zbl 1156.91321 Lasry, Jean-Michel; Lions, Pierre-Louis 1,084 2007 Correlations and bounds for stochastic volatility models. Zbl 1108.62110 Lions, P.-L.; Musiela, M. 48 2007 Global existence of weak solutions to some micro-macro models. Zbl 1117.35312 Lions, Pierre-Louis; Masmoudi, Nader 40 2007 Stochastic homogenization and random lattices. Zbl 1129.60055 Blanc, X.; Le Bris, C.; Lions, P.-L. 38 2007 The energy of some microscopic stochastic lattices. Zbl 1173.82308 Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 32 2007 Atomistic to continuum limits for computational materials science. Zbl 1144.82018 Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 25 2007 Large investor trading impacts on volatility. Zbl 1160.91016 Lions, Pierre-Louis; Lasry, Jean-Michel 17 2007 Two remarks on generalized flows for ordinary differential equations. (Deux remarques sur les flots généralisés d’équations différentielles ordinaires.) Zbl 1132.34043 Hauray, Maxime; Le Bris, Claude; Lions, Pierre-Louis 9 2007 Large investor trading impacts on volatility. Zbl 1153.91428 Lions, Pierre-Louis; Lasry, Jean-Michel 5 2007 Instantaneous self-fulfilling of long-term prophecies on the probabilistic distribution of financial asset values. Zbl 1130.91340 Lions, P.-L.; Lasry, J.-M. 4 2007 Mean field games. I: The stationary case. (Jeux à champ moyen. I: Le cas stationnaire.) Zbl 1153.91009 Lasry, Jean-Michel; Lions, Pierre-Louis 461 2006 Mean field games. II: Finite horizon and optimal control. (Jeux à champ moyen. II: Horizon fini et contrôle optimal.) Zbl 1153.91010 Lasry, Jean-Michel; Lions, Pierre-Louis 428 2006 A variant of stochastic homogenization theory for elliptic operators. (Une variante de la théorie de l’homogénéisation stochastique des opérateurs elliptiques.) Zbl 1103.35014 Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 22 2006 Convexity of solutions of parabolic equations. Zbl 1096.35006 Lions, Pierre-Louis; Musiela, Marek 16 2006 Towards a self-consistent theory of volatility. Zbl 1127.91027 Lions, 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 1095.74006 Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 5 2006 Some properties of diffusion processes with singular coefficients. Zbl 1104.60045 Lions, Pierre-Louis; Musiela, Marek 3 2006 Homogenization of “viscous” Hamilton–Jacobi equations in stationary ergodic media. Zbl 1065.35047 Lions, Pierre-Louis; Souganidis, Panagiotis E. 67 2005 From atoms to crystals: a mathematical journey. Zbl 1136.81371 Le Bris, Claude; Lions, Pierre-Louis 65 2005 Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications. Zbl 1135.35092 Lions, Pierre-Louis; Souganidis, Panagiotis E. 50 2005 On the uniqueness of the solution of the two-dimensional Navier–Stokes equation with a Dirac mass as initial vorticity. Zbl 1083.35092 Gallagher, Isabelle; Gallay, Thierry; Lions, Pierre-Louis 16 2005 Homogenization of the Euler system in a 2D porous medium. Zbl 1072.35032 Lions, P.-L.; Masmoudi, N. 12 2005 Renormalized solutions of some transport equations with partially \(W^{1,1}\) velocities and applications. Zbl 1170.35364 Le Bris, C.; Lions, P.-L. 66 2004 Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting. Zbl 1050.35012 Lions, Pierre-Louis; Souganidis, Panagiotis E. 66 2003 A definition of the ground state energy for systems composed of infinitely many particles. Zbl 1035.82004 Blanc, X.; Le Bris, C.; Lions, P. L. 22 2003 From molecular models to continuum mechanics. Zbl 1028.74005 Blanc, X.; Le Bris, C.; Lions, P.-L. 103 2002 On some periodic Hartree-type models for crystals. Zbl 1005.81101 Catto, I.; Le Bris, C.; Lions, P.-L. 35 2002 Characterization of functions on \(\mathbb{R}^3\) with bounded Newtonian potential. (Caractérisation des fonctions de \(\mathbb{R}^3\) à potentiel newtonien borné.) Zbl 0995.35028 Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 4 2002 From the Boltzmann equations to the equations of incompressible fluid mechanics. I, II. Zbl 0987.76088 Lions, P.-L.; Masmoudi, N. 133 2001 Applications of Malliavin calculus to Monte-Carlo methods in finance. II. Zbl 0973.60061 Fournié, Eric; Lasry, Jean-Michel; Lebuchoux, Jérôme; Lions, Pierre-Louis 81 2001 On the thermodynamic limit for Hartree-Fock type models. Zbl 0994.35115 Catto, I.; Le Bris, C.; Lions, P.-L. 51 2001 Uniqueness of mild solutions of the Navier-Stokes system in \(L^N\). Zbl 1086.35077 Lions, P.-L.; Masmoudi, N. 47 2001 A deterministic particle method for nonlinear diffusion equations. (Une méthode particulaire déterministe pour des équations diffusives non linéaires.) Zbl 0973.65003 Lions, Pierre-Louis; Mas-Gallic, Sylvie 35 2001 Convergence of molecular models to continuum mechanics models. (Convergence de modèles moléculaires vers des modèles de mécanique des milieux continus.) Zbl 0986.74006 Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis 10 2001 Global solutions for some Oldroyd models of non-Newtonian flows. Zbl 0957.35109 Lions, P. L.; Masmoudi, N. 181 2000 Uniqueness of weak solutions of fully nonlinear stochastic partial differential equations. Zbl 0970.60072 Lions, Pierre-Louis; Souganidis, Panagiotis E. 42 2000 Fully nonlinear stochastic PDE with semilinear stochastic dependence. Zbl 0966.60058 Lions, Pierre-Louis; Souganidis, Panagiotis E. 40 2000 Equilibrium statistical theory for nearly parallel vortex filaments. Zbl 1041.76038 Lions, Pierre-Louis; Majda, Andrew 24 2000 On some challenging problems in nonlinear partial differential equations. Zbl 0972.35094 Lions, P.-L. 7 2000 A new class of singular stochastic control problems. (Une classe nouvelle de problèmes singuliers de contrôle stochastique.) Zbl 0971.49015 Lasry, 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 0967.35029 Arisawa, M.; Ishii, H.; Lions, P.-L. 2 2000 Recent mathematical results on the quantum modeling of crystals. Zbl 0998.82036 Catto, I.; Le Bris, C.; Lions, P.-L. 1 2000 Applications of Malliavin calculus to Monte Carlo methods in finance. Zbl 0947.60066 Fournié, Eric; Lasry, Jean-Michel; Lebuchous, Jérôme; Lions, Pierre-Louis 171 1999 Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions. Zbl 0992.35067 Desjardins, B.; Grenier, E.; Lions, P.-L.; Masmoudi, N. 106 1999 A local approach to the incompressible limit. (Une approche locale de la limite incompressible.) Zbl 0937.35132 Lions, Pierre-Louis; Masmoudi, Nader 46 1999 Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations. Zbl 0927.35029 Crandall, M. G.; Kocan, M.; Lions, P. L.; Świȩch, A. 44 1999 On a free boundary barotropic model. Zbl 0917.76073 Lions, P.-L.; Masmoudi, N. 30 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 0931.35126 Lions, Pierre-Louis 16 1999 Comparison results for solutions of elliptic problems via symmetrization. Zbl 0924.35038 Alvino, 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 0937.93058 Laskry, 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 1061.35530 Lions, P.-L.; Souganidis, P. E. 6 1999 Mathematical topics in fluid mechanics. Vol. 2: Compressible models. Zbl 0908.76004 Lions, Pierre-Louis 1,020 1998 Incompressible limit for a viscous compressible fluid. Zbl 0909.35101 Lions, P.-L.; Masmoudi, N. 222 1998 ...and 267 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 15,617 Authors 150 Lions, Pierre-Louis 113 Feireisl, Eduard 106 Alves, Claudianor Oliveira 105 Tang, Xianhua 77 Perthame, Benoît 76 Tang, Chun-Lei 74 Souganidis, Panagiotis E. 65 Cardaliaguet, Pierre 62 Do Ó, João M. 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