Lions Pierre-Louis - CV

CEREMADE

Lions Pierre-Louis

Professeur au Collège de France

Envoyer un email

Bureau : B626

Biographie

Pierre-Louis Lions est un mathématicien français né à Grasse en 1956, lauréat de la médaille Fields en 1994. Il entre à l’Ecole Normale Supérieure en 1975. Il se consacre à la recherche en mathématiques appliquées et obtient son habilitation en 1979 à l’Université Pierre et Marie Curie. De 1979 à 1981, il est chercheur au CNRS puis devient professeur à l’Université de Paris-Dauphine en 1981 et professeur de mathématiques appliquées à l’Ecole Polytechnique de 1992 à 2016. Il est nommé professeur au Collège de France en 2002, titulaire de la chaire “Equations aux dérivées partielles et applications”. Parmi ses travaux, il fut le premier mathématicien à donner une solution complète à l’équation de Boltzmann et il a introduit, en collaboration avec Michael Crandall, la notion de solutions de viscosité dont les domaines d’applications sont multiples. Ces dernières années, en collaboration avec Jean-Michel Lasry, il a introduit et développé la théorie des jeux à champ moyen et ses applications notamment à l’économie et à la finance. Outre la médaille Fields, il a reçu de nombreux prix, il est Docteur Honoris Causa de plusieurs universités et membre de nombreuses académies. Il est commandeur de la Légion d’Honneur. Ses collaborations avec le monde de l’entreprise sont nombreuses et variées en tant que conseiller scientifique, administrateur, responsable de contrats de recherche ou d’actions de mécénats, fondateur de la Start-up MFG Labs aujourd’hui filiale de Havas Media. Il a exercé et exerce de nombreuses responsabilités collectives. Il a également formé de nombreux chercheurs dont Cédric Villani (médaille Fields), B. Perthame (Grand Prix INRIA), N. Masmoudi (Prix Fermat), C. Le Bris (Prix Blaise Pascal), M. Esteban (Présidente de l’ICIAM)…

Publications

Articles

Achdou Y., Han J., Lasry J-M., Lions P-L., Moll B. (2022), Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach, The Review of Economic Studies, vol. 89, n°1, p. 45-86

Bertucci C., Debbah M., Lasry J-M., Lions P-L. (2022), A Spectral Dominance Approach to Large Random Matrices, Journal de mathématiques pures et appliquées, vol. 164, p. 27-56

Achdou Y., Bertucci C., Lasry J-M., Lions P-L., Rostand A., Scheinkman J. (2022), A class of short-term models for the oil industry addressing speculative storage, Finance and Stochastics, vol. 26, p. 631–669

Bertucci C., Lasry J-M., Lions P-L. (2021), Master equation for the finite state space planning problem, Archive for Rational Mechanics and Analysis, vol. 242, p. 327–342

Gassiat P., Gess B., Lions P-L., Souganidis P. (2020), Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians, Probability Theory and Related Fields, vol. 176, p. 421–448

Bertucci C., Lasry J-M., Lions P-L. (2020), Strategic advantages in mean field games with a major player, Comptes rendus. Mathématique, vol. 358, n°2, p. 113-118

Bertucci C., Lasry J., Lions P. (2019), Some remarks on Mean Field Games, Communications in Partial Differential Equations, vol. 44, n°3, p. 205-227

Blanc X., Le Bris C., Lions P-L. (2019), On correctors for linear elliptic homogenization in the presence of local defects, Communications in Partial Differential Equations, vol. 43, n°6, p. 963-997

Friz P., Gassiat P., Lions P-L., Souganidis P. (2017), Eikonal equations and pathwise solutions to fully non-linear SPDEs, Stochastics and Partial Differential Equations: Analysis and Computations, vol. 5, n°2, p. 256-277

Achdou Y., Giraud P-N., Lasry J-M., Lions P-L. (2016), A Long-Term Mathematical Model for Mining Industries, Applied Mathematics and Optimization, vol. 74, n°3, p. 579–618

Blanc X., Le Bris C., Lions P-L. (2015), Local profiles and elliptic problems at different scales with defects, Comptes rendus. Mathématique, vol. 333, n°3, p. 203-208

Achdou Y., Buera F., Lasry J-M., Lions P-L., Moll B. (2014), Partial differential equation models in macroeconomics, Philosophical Transactions. Physical, Mathematical and Engineering Sciences, vol. 372

Porretta A., Lions P-L., Lasry J-M., Cardaliaguet P. (2013), Long Time Average of Mean Field Games with a Nonlocal Coupling, SIAM Journal on Control and Optimization, vol. 51, n°5, p. 3558–3591

Perthame B., Souganidis P., Lions P-L. (2013), Scalar conservation laws with rough (stochastic) fluxes, Stochastics and Partial Differential Equations: Analysis and Computations, vol. 1, n°4, p. 664-686

Lasry J-M., Porretta A., Lions P-L., Cardaliaguet P. (2012), Long time average of mean field games, Networks and Heterogeneous Media, vol. 7, n°2, p. 279-301

Lions P-L., Le Bris C., Blanc X. (2012), From the Newton equation to the wave equation in some simple cases, Networks and Heterogeneous Media, vol. 7, n°1, p. 1-41

Blanc X., Le Bris C., Lions P-L. (2012), A Possible Homogenization Approach for the Numerical Simulation of Periodic Microstructures with Defects, Milan Journal of Mathematics, vol. 80, n°2, p. 351-367

Lions P-L., Souganidis P. (2010), Stochastic homogenization of Hamilton-Jacobi and "Viscous"-Hamilton-Jacobi equations with convex, Communications in Mathematical Sciences, vol. 8, n°2, p. 627-637

Cardaliaguet P., Lions P-L., Souganidis P. (2009), A discussion about the homogenization of moving interfaces, Journal de mathématiques pures et appliquées, vol. 91, n°4, p. 339–363

Le Bris C., Lions P-L. (2008), Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients, Communications in Partial Differential Equations, vol. 33, n°7, p. 1272-1317

Lions P-L., Cancès E., Le Bris C. (2008), Molecular simulation and related topics: some open mathematical problems, Nonlinearity, vol. 21, n°9, p. 165-176

Blanc X., Le Bris C., Lions P-L. (2007), The energy of some microscopic stochastic lattices, Archive for Rational Mechanics and Analysis, vol. 184, n°2, p. 303-339

Le Bris C., Blanc X., Lions P-L. (2007), Atomistic to Continuum limits for computational materials science, ESAIM: Mathematical Modelling and Numerical Analysis, vol. 41, n°2, p. 391-426

Le Bris C., Lions P-L., Blanc X. (2007), Stochastic homogenization and random lattices, Journal de mathématiques pures et appliquées, vol. 88, n°1, p. 34-63

Masmoudi N., Lions P-L. (2007), Global existence of weak solutions to some micro-macro models, Comptes rendus. Mathématique, vol. 345, n°1, p. 15-20

Lasry J-M., Lions P-L. (2007), Instantaneous self-fulfilling of long-term prophecies on the probabilistic distribution of financial asset values, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, vol. 24, n°3, p. 361-368

Hauray M., Le Bris C., Lions P-L. (2007), Deux remarques sur les flots généralisés d'équations différentielles ordinaires, Comptes rendus. Mathématique, vol. 344, n°12, p. 759-764

Lasry J-M., Lions P-L. (2007), Large investor trading impacts on volatility, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, vol. 24, n°2, p. 311-323

Lasry J-M., Lions P-L. (2007), Mean Field Games, Japanese Journal of Mathematics, vol. 2, n°1, p. 229-260

Lions P-L., Musiela M. (2007), Correlations and bounds for stochastic volatility models, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, vol. 24, n°1, p. 1-16

Lions P-L. (2007), Preface ((Special Issue on Molecular Modelling), ESAIM: Mathematical Modelling and Numerical Analysis, vol. 41, n°2, p. 187-188

Musiela M., Lions P-L. (2006), Some Properties of Diffusion Processes with Singular Coefficients, Communications in Applied Analysis, vol. 10, n°1, p. 109-126

Lions P-L., Blanc X., Le Bris C. (2006), Du discret au continu pour des modèles de réseaux aléatoires d'atomes, Comptes rendus. Mathématique, vol. 342, n°8, p. 627-633

Musiela M., Lions P-L. (2006), Convexity of solutions of parabolic equations, Comptes rendus. Mathématique, vol. 342, n°12, p. 915-921

Lions P-L., Lasry J-M. (2006), Jeux à champ moyen. I – Le cas stationnaire, Comptes rendus. Mathématique, vol. 343, n°9, p. 619-625

Lions P-L., Lasry J-M. (2006), Jeux à champ moyen. II – Horizon fini et contrôle optimal, Comptes rendus. Mathématique, vol. 343, n°10, p. 679-684

Blanc X., Lions P-L., Le Bris C. (2006), Une variante de la théorie de l'homogénéisation stochastique des opérateurs elliptiques, Comptes rendus. Mathématique, vol. 343, n°11-12, p. 717-724

Lions P-L., Lasry J-M. (2006), Towards a self-consistent theory of volatility, Journal de mathématiques pures et appliquées, vol. 86, n°6, p. 541-551

Le Bris C., Lions P-L. (2005), From atoms to crystals: a mathematical journey, Bulletin of the American Mathematical Society, n°42, p. 291-363

Lions P-L., Gallagher I., Gallay T. (2005), On the uniqueness of the solution of the two-dimensional Navier–Stokes equation with a Dirac mass as initial vorticity, Mathematische Nachrichten, vol. 278, n°14, p. 1665–1672

Lions P-L., Souganidis P. (2005), Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, vol. 22, n°5, p. 667-677

Lions P-L., Le Bris C. (2004), Renormalized solutions of some transport equations with partially W 1,1 velocities and applications, Annali di Matematica Pura ed Applicata, vol. 183, n°1, p. 97-130

Souganidis P., Lions P-L. (2003), Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting, Communications on Pure and Applied Mathematics, vol. 56, n°10, p. 1501-1524

Catto I., Lions P-L., Le Bris C. (2002), On some periodic Hartree-type models for crystals, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, vol. 19, n°2, p. 143-190

Blanc X., Le Bris C., Lions P-L. (2002), From Molecular Models to Continuum Mechanics, Archive for Rational Mechanics and Analysis, vol. 164, n°4, p. 341-381

Mas-Gallic S., Lions P-L. (2001), Une méthode particulaire déterministe pour des équations diffusives non linéaires, Comptes rendus. Mathématique, vol. 332, n°4, p. 369-376

Le Bris C., Catto I., Lions P-L. (2001), On the thermodynamic limit for Hartree–Fock type models, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, vol. 18, n°6, p. 687-760

Lions P-L., Lasry J-M., Lebuchoux J., Fournié E. (2001), Applications of Malliavin calculus to Monte-Carlo methods in finance. II, Finance and Stochastics, vol. 5, n°2, p. 201-236

Lions P-L., Arisawa M., Ishii H. (2000), A characterization of the existence of solutions for Hamilton—Jacobi equations in ergodic control problems with applications, Applied Mathematics and Optimization, vol. 42, n°1, p. 35-50

Lasry J-M., Lions P-L. (2000), Une classe nouvelle de problèmes singuliers de contrôle stochastique, Comptes rendus. Mathématique, vol. 331, n°11, p. 879-885

Lions P-L., Souganidis P. (2000), Fully nonlinear stochastic PDE with semilinear stochastic dependence, Comptes rendus. Mathématique, vol. 331, n°8, p. 617-624

Lions P-L., Masmoudi N. (2000), Global Solutions for Some Oldroyd Models of Non Newtonian Flows, Chinese Annals of Mathematics, Series B, vol. 21, n°2, p. 131-146

Lions P-L., Alvino A., Matarasso S., Rombetti G. (1999), Comparison results for solutions of elliptic problems via symmetrization, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, vol. 16, n°2, p. 167-188

Lions P-L., Touzi N., Lebuchoux J., Fournié E., Lasry J-M. (1999), Applications of Malliavin calculus to Monte Carlo methods in finance, Finance and Stochastics, vol. 3, n°4, p. 391-412

Lions P-L., Lasry J-M. (1999), Contrôle stochastique avec informations partielles et applications à la Finance, Comptes rendus. Mathématique, vol. 328, n°11, p. 1003-1010

Lions P-L., Swiech A., Kocan M., Crandall M. (1999), Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations, Electronic Journal of Differential Equations, vol. 1999, n°24, p. 1-20

Masmoudi N., Lions P-L. (1999), On a free boundary barotropic model, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, vol. 16, n°3, p. 373-410

Lions P-L., Masmoudi N. (1999), Une approche locale de la limite incompressible, Comptes rendus. Mathématique, vol. 329, n°5, p. 387-392

Lions P-L. (1999), Bornes sur la densité pour les équations de Navier-Stokes compressibles isentropiques avec conditions aux limites de Dirichlet, Comptes rendus. Mathématique, vol. 328, n°8, p. 659-662

Catto I., Lions P-L., Le Bris C. (1998), Sur la limite thermodynamique pour des modèles de type Hartree et Hartree-Fock, Comptes rendus. Mathématique, vol. 327, n°3, p. 259-266

Lions P-L. (1998), Régularité optimale des moyennes en vitesses, II, Comptes rendus. Mathématique, vol. 326, n°8, p. 945-948

Lions P-L. (1998), Régularité et compacité pour des noyaux de collision de Boltzmann sans troncature angulaire, Comptes rendus. Mathématique, vol. 326, n°1, p. 37-41

Souganidis P., Lions P-L. (1998), Fully nonlinear stochastic partial differential equations, Comptes rendus. Mathématique, vol. 326, n°9, p. 1085-1092

Masmoudi N., Lions P-L. (1998), Incompressible limit for a viscous compressible fluid, Journal de mathématiques pures et appliquées, vol. 77, n°6, p. 585-627

Lions P-L., Arisawa M. (1998), On ergodic stochastic control, Communications in Partial Differential Equations, vol. 23, n°11-12, p. 333-358

Lions P-L., Souganidis P. (1998), Fully nonlinear stochastic partial differential equations: non-smooth equations and applications, Comptes rendus. Mathématique, vol. 327, n°8, p. 735-741

Lions P-L. (1998), Identification du cône dual des fonctions convexes et applications, Comptes rendus. Mathématique, vol. 326, n°12, p. 1385-1390

Lions P-L. (1998), Sur les équations différentielles ordinaires et les équations de transport, Comptes rendus. Mathématique, vol. 326, n°7, p. 833-838

Masmoudi N., Lions P-L. (1998), Unicité des solutions faibles de Navier-Stokes dans LN (Omega), Comptes rendus. Mathématique, vol. 327, n°5, p. 491-496

Alvarez O., Lasry J-M., Lions P-L. (1997), Convex viscosity solutions and state constraints, Journal de mathématiques pures et appliquées, vol. 76, n°3, p. 265-288

Lions P-L., Toscani G. (1997), Diffusive limit for finite velocity Boltzmann kinetic models, Revista Matematica Iberoamericana, vol. 13, n°3, p. 473-513

Lions P-L., Ferone V., Alvino A. (1997), Convex symmetrization and applications, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, vol. 14, n°2, p. 275-293

Chambolle A., Lions P-L. (1997), Image recovery via total variation minimization and related problems, Numerische Mathematik, vol. 76, n°2, p. 167-188

Ishii H., Lions P-L., Arisawa M. (1997), Un contre-exemple pour la théorie du contrôle ergodique en dimension infinie, Comptes rendus. Mathématique, vol. 325, n°1, p. 37-41

Souganidis P., Lions P-L., Perthame B. (1996), Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates, Communications on Pure and Applied Mathematics, vol. 49, n°6, p. 599-638

Arisawa M., Lions P-L. (1996), Continuity of admissible trajectories for state constraints control problems, Discrete and Continuous Dynamical Systems, vol. 2, n°3, p. 297-305

Catto I., Le Bris C., Lions P-L. (1996), Limite thermodynamique pour des modèles de type Thomas-Fermi, Comptes rendus. Mathématique, vol. 322, p. 357-364

Villani C., Lions P-L. (1995), Régularité optimale de racines carrées, Comptes rendus. Mathématique, n°321, p. 1537-1541

Lions P-L., Lasry J-M. (1995), Grandes déviations pour des processus de diffusion couplés par un processus de sauts, Comptes rendus. Mathématique, vol. 321, n°7, p. 849-854

Lions P-L. (1995), Régularité optimale des moyennes en vitesses, Comptes rendus. Mathématique, vol. 320, n°8, p. 911-915

Lions P-L., Souganidis P. (1995), Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations, Numerische Mathematik, vol. 69, n°4, p. 441-470

Perthame B., Lions P-L., Tadmor E. (1994), Kinetic formulation of the isentropic gas dynamics and p-systems, Communications in Mathematical Physics, vol. 163, n°2, p. 415-431

Catto I., Lions P-L. (1993), Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. Part 4 : Binding of neutral systems for the Hartree model, Communications in Partial Differential Equations, vol. 18, n°7-8, p. 1149-1159

Lions P-L., Guichard F., Alvarez L., Morel J-M. (1993), Axioms and fundamental equations of image processing, Archive for Rational Mechanics and Analysis, vol. 123, n°3, p. 199-257

Tourin A., Lions P-L., Rouy E. (1993), Shape-from-shading, viscosity solutions and edges, Numerische Mathematik, vol. 64, n°1, p. 323-353

Catto I., Lions P-L. (1993), Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. Part 3 : Binding of neutral subsystems, Communications in Partial Differential Equations, vol. 18, n°3-4, p. 381-429

Catto I., Lions P-L. (1993), Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. Part 2 : Stability is equivalent to the binding of neutral subsystems, Communications in Partial Differential Equations, vol. 18, n°1-2, p. 305-354

Pulvirenti M., Marchioro C., Lions P-L., Caglioti E. (1992), A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description, Communications in Mathematical Physics, vol. 43, n°3, p. 501-525

Catto I., Lions P-L. (1992), A necessary and sufficient condition for the stability of general molecular systems, Communications in Partial Differential Equations, vol. 17, n°7-8, p. 1051-1110

Lions P-L. (1992), On the existence and convergence of solutions of Boltzmann equations, Rendiconti del Seminario Matematico e Fisico di Milano, vol. 62, n°1, p. 115-125

Morel J-M., Lions P-L., Coll T., Catté F. (1992), Image Selective Smoothing and Edge Detection by Nonlinear Diffusion, SIAM Journal on Numerical Analysis, vol. 29, n°1, p. 182-193

Duffie D., Lions P-L. (1992), PDE solutions of stochastic differential utility, Journal of Mathematical Economics, vol. 21, n°6, p. 577-606

DiPerna R., Lions P-L. (1991), Global solutions of Boltzmann's equation and the entropy inequality, Archive for Rational Mechanics and Analysis, vol. 114, n°1, p. 47-55

Lions P-L., Perthame B. (1991), Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Inventiones Mathematicae, vol. 105, n°1, p. 415-430

Crandall M., Lions P-L. (1991), Viscosity solutions of Hamilton-Jacobi equations in infinite dimensions. V. Unbounded linear terms and B-continuous solutions, Journal of Functional Analysis, vol. 97, n°2, p. 417-465

Barles G., Lions P-L. (1991), Fully nonlinear Neumann type boundary conditions for first-order Hamilton–Jacobi equations, Nonlinear Analysis, vol. 16, n°2, p. 143-153

Crandall M., Lions P-L. (1990), Viscosity solutions of Hamilton-Jacobi equations in infinite dimensions. IV. Hamiltonians with unbounded linear terms, Journal of Functional Analysis, vol. 90, n°2, p. 237-283

Lions P-L., Ishii H. (1990), Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, Journal of Differential Equations, vol. 83, n°1, p. 26-78

Lions P-L., Larrouturou B., Berestycki H. (1990), Multi-dimensional travelling-wave solutions of a flame propagation model, Archive for Rational Mechanics and Analysis, vol. 111, n°1, p. 33-49

Catto I., Lions P-L. (1990), La stabilité des molécules et la liaison des atomes pour des modèles de type Thomas-Fermi ou Hartree, Comptes rendus. Mathématique, vol. 311, p. 193-198

Crandall M., Lions P-L., Souganidis P. (1989), Maximal solutions and universal bounds for some partial differential equations of evolution, Archive for Rational Mechanics and Analysis, vol. 105, n°2, p. 163-190

Lions P-L. (1989), On Hartree and Hartree-Fock equations in atomic and nuclear physics, Computer Methods in Applied Mechanics and Engineering, vol. 75, n°1-3, p. 53-60

Lions P-L. (1989), Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. III. Uniqueness of viscosity solutions for general second-order equations, Journal of Functional Analysis, vol. 86, n°1, p. 1-18

DiPerna R., Lions P-L. (1989), Ordinary differential equations, transport theory and Sobolev spaces, Inventiones Mathematicae, vol. 98, n°3, p. 511-547

Lions P-L., Trombetti G., Alvino A. (1989), On optimization problems with prescribed rearrangements, Nonlinear Analysis, vol. 13, n°2, p. 185-220

Lions P-L., Lasry J-M. (1989), Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints, Mathematische Annalen, vol. 283, n°4, p. 583-630

Lions P-L., Golse F., Sentis R., Perthame B. (1988), Regularity of the moments of the solution of a Transport Equation, Journal of Functional Analysis, vol. 76, n°1, p. 110-125

Lions P-L., DiPerna R. (1988), On the Fokker-Planck-Boltzmann equation, Communications in Mathematical Physics, vol. 120, n°1, p. 1-23

Lions P-L. (1988), Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part I: the case of bounded stochastic evolutions, Acta Mathematica, vol. 161, n°1, p. 243-278

Lions P-L. (1987), Solutions of Hartree-Fock equations for Coulomb systems, Communications in Mathematical Physics, vol. 109, n°1, p. 33-97

Perthame B., Lions P-L. (1987), Remarks on Hamilton-Jacobi equations with measurable time-dependent Hamiltonians, Nonlinear Analysis, vol. 11, n°5, p. 613-621

Crandall M., Lions P-L. (1986), On existence and uniqueness of solutions of Hamilton-Jacobi equations, Nonlinear Analysis, vol. 10, n°4, p. 353-370

Crandall M., Lions P-L. (1986), Hamilton-Jacobi equations in infinite dimensions. II. Existence of viscosity solutions, Journal of Functional Analysis, vol. 65, n°3, p. 368-405

Perthame B., Lions P-L. (1986), Quasi-Variational Inequalities and Ergodic Impulse Control, SIAM Journal on Control and Optimization, vol. 24, n°4, p. 604-615

Trudinger N., Lions P-L. (1986), Linear oblique derivative problems for the uniformly elliptic Hamilton-Jacobi-Bellman equation, Mathematische Zeitschrift, vol. 191, n°1, p. 1-15

Lions P-L., Souganidis P. (1986), Differential Games and Directional Derivatives of Viscosity Solutions of Isaacs’ Equations II, SIAM Journal on Control and Optimization, vol. 24, n°5, p. 1086-1089

Lasry J-M., Lions P-L. (1986), A remark on regularization in Hilbert spaces, Israel Journal of Mathematics, vol. 55, n°3, p. 257-266

Crandall M., Lions P-L. (1986), Hamilton-Jacobi equations in infinite dimensions, III, Journal of Functional Analysis, vol. 68, n°2, p. 214-247

Crandall M., Lions P-L. (1985), Viscosity Solutions of Hamilton-Jacobi Equations in Banach Spaces, North-Holland Mathematics Studies, vol. 110, p. 115-119

Crandall M., Lions P-L. (1985), Hamilton-Jacobi equations in infinite dimensions I. Uniqueness of viscosity solutions, Journal of Functional Analysis, vol. 62, n°3, p. 379-396

Lions P-L. (1985), Sur les equations de Monge-Ampère, Archive for Rational Mechanics and Analysis, vol. 89, n°2, p. 93-122

Lions P-L. (1985), Two remarks on Monge-Ampere equations, Annali di Matematica Pura ed Applicata, vol. 142, n°1, p. 263-275

Lions P-L., Souganidis P. (1984), Differential Games, Optimal Control and Directional Derivatives of Viscosity Solutions of Bellman’s and Isaacs’ Equations, SIAM Journal on Control and Optimization, vol. 23, n°4, p. 566-583

Lions P-L. (1984), Structure of the set of steady-state solutions and asymptotic behaviour of semilinear heat equations, Journal of Differential Equations, vol. 53, n°3, p. 362-386

Berestycki H., Lions P-L. (1983), Nonlinear scalar field equations, II existence of infinitely many solutions, Archive for Rational Mechanics and Analysis, vol. 82, n°4, p. 347-375

Lions P-L. (1983), Bifurcation and optimal stochastic control, Nonlinear Analysis, vol. 7, n°2, p. 177-207

Lions P-L. (1983), On the Hamilton-Jacobi-Bellman equations, Acta Applicandae Mathematicae, vol. 1, n°1, p. 17-41

Lions P-L. (1983), Sur les equations de Monge-Ampere. I, Manuscripta Mathematica, vol. 41, n°1-3, p. 1-43

Berestycki H., Lions P-L. (1983), Nonlinear scalar field equations, I existence of a ground state, Archive for Rational Mechanics and Analysis, vol. 82, n°4, p. 313-345

Lions P-L., Esteban M. (1983), A compactness lemma, Nonlinear Analysis, vol. 7, n°4, p. 381-385

Lions P-L. (1982), Asymptotic behavior of some nonlinear heat equations, Physica D : Nonlinear Phenomena, vol. 5, n°2-3, p. 293-306

Lions P-L. (1982), Symétrie et compacité dans les espaces de Sobolev, Journal of Functional Analysis, vol. 49, n°3, p. 315-334

Cazenave T., Lions P-L. (1982), Orbital stability of standing waves for some nonlinear Schrödinger equations, Communications in Mathematical Physics, vol. 85, n°4, p. 549-561

Ouvrages

Cardaliaguet P., Delarue F., Lasry J-M., Lions P-L. (2019), The master equation and the convergence problem in mean field games De Gruyter, 224 p.

Cousin A., Crépey S., Guéant O., Hobson D., Jeanblanc M., Lasry J-M., Laurent J-P., Lions P-L., Tankov P. (2011), Paris-Princeton Lectures on Mathematical Finance 2010, Berlin: Springer, 359 p.

Catto I., Le Bris C., Lions P-L. (1998), Mathematical theory of thermodynamic limits. Thomas- Fermi type models, Oxford: Clarendon Press, 292 p.

Lions P-L. (1998), Mathematical Topics in Fluid Mechanics. Volume 2: Compressible Models, Oxford: Clarendon Press, 364 p.

Lions P-L. (1997), On Euler equations and statistical physics, Pise: Scuola normale superiore, 69 p.

Lions P-L. (1996), Mathematical Topics in Fluid Mechanics: Volume 1: Incompressible Models, Oxford: Clarendon Press, 256 p.

Chapitres d'ouvrage

Guéant O., Lasry J-M., Lions P-L. (2010), Mean Field Games and Oil Production, in Fessler, Damien; Lautier, Delphine; Lasry, Jean-Michel, The Economics of Sustainable Development, Paris: Economica, p. 368

Catto I., Lions P-L., Le Bris C. (2000), Recent mathematical results on the quantum modeling of crystals, in Mireille Defranceschi, Claude Le Bris, Mathematical models and methods for ab initio quantum chemistry, Edimbourg: Springer, p. 95-120

Lions P-L. (2000), On Some Challenging Problems in Nonlinear Partial Differential Equations, in Arnold, Vladimir, Mathematics: frontiers and perspectives, Providence (RI): American Mathematical Society, p. 459

Fournié E., Lions P-L., Lasry J-M. (1997), Some nonlinear methods for studying far-from-the-money contingent claims, in Talay, Denis, Numerical methods in finance, Cambridge: Cambridge University Press, p. 326

Communications avec actes

Lions P-L., Guéant O., Lasry J-M. (2011), Mean Field Games and Applications, in Tankov, Peter, Paris-Princeton Lectures on Mathematical Finance 2010, Paris, Springer, 359 p.

Lasry J-M., Lions P-L. (2007), Large investor trading impacts on volatility, in Taflin, Erik, Paris-Princeton Lectures on Mathematical Finance 2004, Berlin, Springer, 173-190 p.

Souganidis P., Perthame B., Lions P-L. (1996), Weak Stability of Isentropic Gas Dynamics for y = 5-3., in Alvino, Angelo, Progress in Elliptic and Parabolic Partial Differential Equations, New York, Longman, 223 p.

Lions P-L. (1986), Dynamic programming and the use of viscosity solutions, in , 25th IEEE Conference on Decision and Control, 1986. Proceedings, Athènes, IEEE - Institute of Electrical and Electronics Engineers, 1680-1681 p.

Communications sans actes

Lions P-L., Perthame B., Souganidis P. (2012), Stochastic averaging lemmas for kinetic equations, Séminaire Laurent Schwartz — EDP et applications, Palaiseau, France

Lions P-L., Souganidis P. (1998), Equations aux dérivées partielles stochastiques nonlinéaires et solutions de viscosité, Séminaire "Equations aux dérivées partielles", Ecole Polytechnique, Palaiseau, France

Prépublications / Cahiers de recherche

Bertucci C., Lasry J-M., Lions P-L. (2024), A spectral dominance approach to large random matrices: part II, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 27 p.

Bertucci C., Lasry J-M., Lions P-L. (2023), On Lipschitz solutions of mean field games master equations, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 29 p.

Bertucci C., Lasry J-M., Lions P-L. (2022), A singular infinite dimensional Hamilton-Jacobi-Bellman equation arising from a storage problem, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 19 p.

Gassiat P., Gess B., Lions P-L., Souganidis P. (2022), Long-time behaviour of stochastic Hamilton-Jacobi equations, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 37 p.

Lions P-L., Seeger B., Souganidis P. (2020), Interpolation results for pathwise Hamilton-Jacobi equations, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 50 p.

Lasry J-M., Guéant O., Lions P-L. (2008), Application of Mean Field Games to Growth Theory, Paris, Université Paris-Dauphine, 17 p.

Lions P-L., Lasry J-M. (2000), A new class of singular stochastic control problems, Cahiers du CEREMADE, 12 p.

Retour à la liste