P. Lions

Pierre-Louis Lions, P. Lions, P. L. Lions, 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

Lp regularity of velocity averages

Pierre-Louis Lions, Y. Meyer, P. Lions, 1991 .

Regularity of the moments of the solution of a Transport Equation

Pierre-Louis Lions, François Golse, Benoît Perthame, 1988 .

On the Fokker-Planck-Boltzmann equation

P. Lions, R. J. Diperna, R. J. DiPerna, 1988 .

Uniqueness of weak solutions of fully nonlinear stochastic partial differential equations

Panagiotis E. Souganidis, Pierre-Louis Lions, P. Souganidis, 2000 .

From atoms to crystals: a mathematical journey

Pierre-Louis Lions, Claude Le Bris, P. Lions, 2005 .

Nonequilibrium Problems in Many-Particle Systems

S. Varadhan, P. Lions, P. Markowich, 1993 .

A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description

Emanuele Caglioti, M. Pulvirenti, Pierre-Louis Lions, 1992 .

Mathematical Topics in Fluid Mechanics: Volume 2: Compressible Models

Pierre-Louis Lions, P. Lions, 1998 .

edu Partial differential equation models in macroeconomics

Francisco J. Buera, P. Lions, Benjamin Moll, 2014 .

Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications

Panagiotis E. Souganidis, Pierre-Louis Lions, P. Souganidis, 2005 .

Homogenization of the backward-forward meanfield games systems in periodic environments

P. Souganidis, P. Lions, 2019, Rendiconti Lincei - Matematica e Applicazioni.

Speed of propagation for Hamilton–Jacobi equations with multiplicative rough time dependence and convex Hamiltonians

P. Souganidis, P. Lions, Paul Gassiat, 2018, Probability Theory and Related Fields.

Nonlinear second-order elliptic equations with jump discontinuous coefficients. I. Quasilinear equations

P. Lions, N. Kutev, 1992 .

Production Capacity issues and "Time to Build" in Oil Production

P. Lions, 2011 .

A class of short-term models for the oil industry that accounts for speculative oil storage

P. Lions, J. Lasry, J. Scheinkman, 2022, Finance and Stochastics.

A special class of stationary flows for two-dimensional euler equations: A statistical mechanics description. Part II

P. Lions, E. Caglioti, M. Pulvirenti, 1995 .

The Dynamics of Inequality The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters

P. Lions, 2016 .

User’s guide to viscosity solutions of second order partial differential equations

P. Lions, M. Crandall, H. Ishii, 1992, math/9207212.

On Euler equations and statistical physics

P. Lions, 1997 .

MULTIPLICITY OF POSITIVE RADIAL SOLUTIONS OF A QUASILINEAR ELLIPTIC PROBLEM IN A BALL*

P. Lions, K. Schmitt, D. G. Figueiredo, 2009 .

Simulating numerically the Krusell-Smith model with neural networks

P. Lions, J. Lasry, Y. Achdou, 2022, 2211.07698.

Partial differential equation models in macroeconomics

Pierre-Louis Lions, Yves Achdou, Jean-Michel Lasry, 2014, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

A Long-Term Mathematical Model for Mining Industries

P. Lions, J. Lasry, Y. Achdou, 2016, Applied Mathematics & Optimization.

Speed of propagation for Hamilton–Jacobi equations with multiplicative rough time dependence and convex Hamiltonians

P. Souganidis, P. Lions, Paul Gassiat, 2019, Probability Theory and Related Fields.

Long-time behaviour of stochastic Hamilton-Jacobi equations

P. Souganidis, P. Lions, Paul Gassiat, 2022, 2211.12099.

A class of short-term models for the oil industry addressing speculative storage

P. Lions, J. Lasry, J. Scheinkman, 2020, 2003.11790.

Hartree-Fock theory in nuclear physics

P. Lions, D. Gogny, Analyse Numérique, 1986 .

Mean Field Games and Applications

Olivier Guéant, Pierre-Louis Lions, Jean-Michel Lasry, 2011 .

Minimization problems in L1(R3)

P. Lions, 1981 .

Some asymptotic problems in fully nonlinear elliptic equations and stochastic control

P. Lions, R. Jensen, 1984 .

From Molecular Models¶to Continuum Mechanics

X. Blanc, P. Lions, C. Bris, 2002 .

Homogenization of “Viscous” Hamilton–Jacobi Equations in Stationary Ergodic Media

Panagiotis E. Souganidis, Pierre-Louis Lions, P. Souganidis, 2005 .

Nonlinear scalar field equations, I existence of a ground state

Pierre-Louis Lions, Henri Berestycki, P. Lions, 1983 .

UNIQUENESS OF MILD SOLUTIONS OF THE NAVIER-STOKES SYSTEM IN LN

P. Lions, N. Masmoudi, 2001 .

Nonlinear scalar field equations, II existence of infinitely many solutions

Pierre-Louis Lions, Henri Berestycki, P. Lions, 1983 .

Stationary solutions of nonlinear Schr?odinger equations with an external magnetic field

P. Lions, M. Esteban, P. Esteban, 1989 .

Interpolation results for pathwise Hamilton-Jacobi equations

P. Souganidis, P. Lions, B. Seeger, 2020, Indiana University Mathematics Journal.

Compactness in Boltzmann’s equation via Fourier integral operators and applications. III

P. Lions, P. L. Lions, 1994 .

The Choquard equation and related questions

P. Lions, P. L. Lions, 1980 .

Sobolev imbedding theorems in borderline cases

P. Lions, N. Fusco, C. Sbordone, 1996 .

Optimal control of reflected diffusion processes

P. Lions, 1984 .

On the existence of a positive solution of semilinear elliptic equations in unbounded domains

Pierre-Louis Lions, Abbas Bahri, P. Lions, 1997 .

On correctors for linear elliptic homogenization in the presence of local defects: The case of advection–diffusion

P. Lions, C. Bris, C. Le Bris, 2018, Journal de Mathématiques Pures et Appliquées.

Local Profiles for Elliptic Problems at Different Scales: Defects in, and Interfaces between Periodic Structures

P. Lions, C. Bris, C. Le Bris, 2015 .

On optimization problems with prescribed rearrangements

Pierre-Louis Lions, Angelo Alvino, P. Lions, 1989 .

Exponential Decay for Soft Potentials near Maxwellian

Robert M. Strain, P. Lions, Yan Guo, 2022 .

On Some Recent Methods for Nonlinear Partial Differential Equations

P. Lions, 1995 .

On some periodic Hartree-type models for crystals

Pierre-Louis Lions, Isabelle Catto, P. Lions, 2002 .

Elliptic equations and Steiner symmetrization

P. Lions, A. Alvino, J. I. Díaz, 1996 .

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

Pierre-Louis Lions, Isabelle Catto, P. Lions, 1993 .

A ecessary and Sufficient Condition for The Stability of General molecular Systems

Pierre-Louis Lions, Isabelle Catto, P. Lions, 1992 .

Solutions of Hartree-Fock equations for Coulomb systems

Pierre-Louis Lions, P. Lions, 1987 .

From quantum electrodynamics to mean-field theory. II. Variational stability of the vacuum of quantum electrodynamics in the mean-field approximation

P. Lions, P. Chaix, D. Iracane, 1989 .

Compactness and Topological Methods for some Nonlinear Variational Problems of Mathematical Physics

P. Lions, 1982 .

Some applications of the method of super and subsolutions

H. Berestycki, P. Lions, H. Berestycki, 1980 .

The Mathematical Theory of Thermodynamic Limits: Thomas--Fermi Type Models

Pierre-Louis Lions, Claude Le Bris, Isabelle Catto, 1998 .

On Positive Solutions of Semilinear Elliptic Equations in Unbounded Domains

P. Lions, 1988 .

A discussion about the homogenization of moving interfaces

Panagiotis E. Souganidis, Pierre-Louis Lions, Pierre Cardaliaguet, 2009 .

Fully nonlinear second order elliptic equations with large zeroth order coefficient

P. Lions, L. Evans, 1981 .

From the Boltzmann Equations¶to the Equations of¶Incompressible Fluid Mechanics, I

Pierre-Louis Lions, Nader Masmoudi, P. Lions, 2001 .

Image restoration by constrained total variation minimization and variants

Antonin Chambolle, Pierre-Louis Lions, P. Lions, 1995, Optics & Photonics.

Comparison results for elliptic and parabolic equations via symmetrization: a new approach

P. Lions, A. Alvino, G. Trombetti, 1991, Differential and Integral Equations.

Comparison results for elliptic and parabolic equations via Schwarz symmetrization

Pierre-Louis Lions, Angelo Alvino, P. Lions, 1990 .

A remark on comparison results via symmetrization

P. Lions, A. Alvino, G. Trombetti, 1986, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

Equilibrium statistical theory for nearly parallel vortex filaments

P. Lions, A. Majda, 2000 .

Existence and uniqueness of solutions to Fokker-Planck type equations with irregular coefficients C .

P. Lions, C. Bris, 2007 .

Global solutions of kinetic models and related questions

P. Lions, 1993 .

On Hartree and Hartree-Fock equations in atomic and nuclear physics

P. Lions, 1989 .

A Long-Term Mathematical Model for Mining Industries

P. Lions, J. Lasry, Y. Achdou, 2016 .

Efficiency of the price formation process in presence of high frequency participants: a mean field game analysis

P. Lions, J. Lasry, A. Lachapelle, 2015, Mathematics and Financial Economics.

An Impulsive Control Problem with State Constraint

B. Perthame, P. Lions, 1989 .

Linear oblique derivative problems for the uniformly elliptic Hamilton-Jacobi-Bellman equation

P. Lions, N. Trudinger, 1986 .

On mathematical finance

Pierre-Louis Lions, P. Lions, 2000 .

The asymptotics of stochastically perturbed reaction-diffusion equations and front propagation

P. Souganidis, P. Lions, 2019, 1909.05673.

On the thermodynamic limit for Hartree–Fock type models

Pierre-Louis Lions, Isabelle Catto, P. Lions, 2001 .

The Energy of Some Microscopic Stochastic Lattices

P. Lions, C. Bris, X. Blanc, 2007 .

Recent mathematical results on the quantum modeling of crystals

P. Lions, C. Bris, I. Catto, 2000 .

Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. Part 4: Binding of neutral systems for the Hartree model

Pierre-Louis Lions, Isabelle Catto, P. Lions, 1993 .

A Definition of the Ground State Energy for Systems Composed of Infinitely Many Particles

P. Lions, C. Bris, C. Le Bris, 2003 .

Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach

Pierre-Louis Lions, Yves Achdou, Jean-Michel Lasry, 2017, The Review of Economic Studies.

Optimal control of conditioned processes with feedback controls

Mathieu Lauriere, Pierre-Louis Lions, Yves Achdou, 2019, Journal de Mathématiques Pures et Appliquées.

Multi-dimensional travelling-wave solutions of a flame propagation model

P. Lions, H. Berestycki, B. Larrouturou, 1990 .

Boundary regularity for some nonlinear elliptic degenerate equations

P. Lions, H. Brezis, 1979 .

Existence of Stationary States in Nonlinear Scalar Field Equations

P. Lions, H. Berestycki, 1980 .

Long Time Average of Mean Field Games with a Nonlocal Coupling

Pierre-Louis Lions, Pierre Cardaliaguet, Jean-Michel Lasry, 2013, SIAM J. Control. Optim..

Long time average of mean field games

Pierre-Louis Lions, Pierre Cardaliaguet, Jean-Michel Lasry, 2012, Networks Heterog. Media.

Parabolic Equations with Irregular Data and Related Issues

P. Lions, C. Bris, 2019 .

Diffusive limit for finite velocity Boltzmann kinetic models

Pierre-Louis Lions, Giuseppe Toscani, P. Lions, 1997 .

Heterogeneous Agent Models in Continuous Time

Pierre-Louis Lions, Yves Achdou, Jean-Michel Lasry, 2013 .

From the Boltzmann Equations¶to the Equations of¶Incompressible Fluid Mechanics, II

P. Lions, N. Masmoudi, P.-L. Lions, 2001 .

Optimal control of stochastic integrals and Hamilton Jacobi-Bellman equations

P. Lions, J. Menaldi, 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

Scalar conservation laws with rough (stochastic) fluxes: the spatially dependent case

Panagiotis E. Souganidis, Pierre-Louis Lions, Benoit Perthame, 2014, Stochastic Partial Differential Equations: Analysis and Computations.

Scalar conservation laws with rough (stochastic) fluxes

Panagiotis E. Souganidis, Pierre-Louis Lions, Benoit Perthame, 2013, Stochastic Partial Differential Equations: Analysis and Computations.

Asymptotic behavior of some nonlinear heat equations

P. Lions, 1982 .

The concentration-compactness principle in the calculus of variations. The locally compact case, part 2

P. Lions, W., Strauss, 1984 .

Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. Part 3 : Binding of neutral subsystems

Pierre-Louis Lions, Isabelle Catto, P. Lions, 1993 .

Viscosity solutions of Hamilton-Jacobi equations

P. Lions, M. Crandall, 1983 .

Structure of the set of steady-state solutions and asymptotic behaviour of semilinear heat equations

Pierre-Louis Lions, P. Lions, 1984 .

Maximal solutions and universal bounds for some partial differential equations of evolution

P. Souganidis, P. Lions, M. Crandall, 1989 .

Conditions at infinity for boltzmann's equation.

P. Lions, 1994 .

Isolated singularities in semilinear problems

P. Lions, 1980 .

Solutions of superlinear elliptic equations and their morse indices

P. Lions, A. Bahri, 1992 .

Existence and non-existence results for semilinear elliptic problems in unbounded domains

P. Lions, M. Esteban, 1982, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

Regularizing effects for first-order hamilton-jacobi equations

P. Lions, 1985 .

Morse index of some min-max critical points

P. Lions, A. Bahri, 1988 .

On the Existence of Positive Solutions of Semilinear Elliptic Equations

P. Lions, 1982 .

Bifurcation and optimal stochastic control

P. Lions, 1983 .

Positive solutions of innomogeneous elliptic boundary value problems in the half space

P. Lions, Xiping Zhu, A. Bahri, 1990 .

On Pairs of Positive Solutions for a Class of Semilinear Elliptic Problems

P. Lions, D. G. Figueiredo, 1985 .

Skyrmions and symmetry

P. Lions, M. Esteban, 1988 .

The Optimal Strategy in the Control Problem Associated with the Hamilton–Jacobi–Bellman Equation

P. Lions, A. Friedman, 1980 .

Two remarks on Monge-Ampere equations

P. Lions, 1985 .

Isoperimetric inequalities for convex cones

Pierre-Louis Lions, Filomena Pacella, P. Lions, 1990 .

Convex symmetrization and applications

Pierre-Louis Lions, Angelo Alvino, P. Lions, 1997 .

Two remarks on the convergence of convex functions and monotone operators

P. Lions, 1978 .

Resolution analytique des problemes de Bellman-Dirichlet

P. Lions, 1981 .

Sum probleils related to the relliian-dzrzchlet equation for two opepators

P. Lions, 1980 .

THE Neumann problem for equations of Monge-Ampère type

Pierre-Louis Lions, Neil S. Trudinger, P. Lions, 1986 .

On the uniqueness of the solution of the two‐dimensional Navier–Stokes equation with a Dirac mass as initial vorticity

P. Lions, T. Gallay, I. Gallagher, 2004, math/0410344.

Sharp existence results for a class of semilinear elliptic problems

P. Lions, H. Berestycki, 1981 .

Correctors for the homogenization of Hamilton‐Jacobi equations in the stationary ergodic setting

Panagiotis E. Souganidis, Pierre-Louis Lions, P. Souganidis, 2003 .

Scalar conservation laws with rough (stochastic) fluxes: the spatially dependent case

P. Souganidis, B. Perthame, P. Lions, 2014, Stochastic Partial Differential Equations: Analysis and Computations.

Scalar conservation laws with rough (stochastic) fluxes

P. Souganidis, B. Perthame, P. Lions, 2013, Stochastic Partial Differential Equations: Analysis and Computations.

Linear and nonlinear transport equations with coordinate-wise increasing velocity fields

P. Lions, B. Seeger, 2023, Annales de l'Institut Henri Poincaré C, Analyse non linéaire.

Transport equations and flows with one-sided Lipschitz velocity fields

P. Lions, B. Seeger, 2023, 2306.13288.

Hamilton-Jacobi Equations in Infinite Dimensions. Part 1. Uniqueness of Viscosity Solutions,

P. Lions, M. Crandall, P L Lions, 1984 .

Master Equation for the Finite State Space Planning Problem

Pierre-Louis Lions, Charles Bertucci, Jean-Michel Lasry, 2020, Archive for Rational Mechanics and Analysis.

A singular infinite dimensional Hamilton-Jacobi-Bellman equation arising from a storage problem

P. Lions, J. Lasry, Charles Bertucci, 2022, 2210.02780.

Extended mean-field games

P. Souganidis, P. Lions, 2020 .

Some remarks on mean field games

Pierre-Louis Lions, Charles Bertucci, Jean-Michel Lasry, 2018, Communications in Partial Differential Equations.

Dimension reduction techniques in deterministic mean field games

P. Lions, J. Lasry, B. Seeger, 2021, Communications in Partial Differential Equations.

Transmit Strategies for Massive Machine-Type Communications based on Mean Field Games

Mérouane Debbah, Pierre-Louis Lions, Spyridon Vassilaras, 2018, 2018 15th International Symposium on Wireless Communication Systems (ISWCS).

R.J. Diperna* Pierre-Louis Lions GLOBAL WEAK SOLUTIONS OF KINETIC EQUATIONS

P. Lions, R. J. Diperna, 2008 .

M ay 2 02 1 DIMENSION REDUCTION TECHNIQUES IN DETERMINISTIC MEAN FIELD GAMES

P. Lions, J. Lasry, B. Seeger, 2021 .

Jacobians and Hardy spaces

P. Lions, 1991 .

The Acoustic Limit for the Boltzmann Equation

François Golse, Claude Bardos, C. David Levermore, 2000 .

Stochastic homogenization of Hamilon-Jacobi and "viscous"-Hamilton-Jacobi equations with convex nonlinearities -- Revisited

P. Souganidis, P. Lions, 2010 .

Stochastic differential systems, stochastic control theory and applications

Wendell H. Fleming, P. L. Lions, W. Fleming, 1988 .

Di usive limit for nite velocity Boltzmann kinetic models

P. Lions, G. Toscani, 2010 .

Time decy, propagarion of low moments and dispersive

B. Perthame, P. Lions, 1996 .

PDE Models in Macroeconomics

Pierre-Louis Lions, Yves Achdou, Jean-Michel Lasry, 2014 .

Application of Mean Field Games to Growth Theory

Olivier Guéant, Pierre-Louis Lions, Jean-Michel Lasry, 2008 .

On correctors for linear elliptic homogenization in the presence of local defects

P. Lions, C. Bris, Xavier Blanc, 2018, Communications in Partial Differential Equations.

Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations.

P. Lions, L. Evans, M. Crandall, 1984 .

Dynamic programming and the use of viscosity solutions

P. Lions, 1986, 1986 25th IEEE Conference on Decision and Control.

A remark on Bony maximum principle

P. Lions, P.-L. Lions, 1983 .

Viscosity Solutions of Second-Order Equations, Stochastic Control and Stochastic Differential Games

P. Souganidis, P. Lions, 1988 .

Recent Progress on First Order Hamilton-Jacobi Equations

P. Lions, 1987 .

Optimal control of reflected diffusion processes : An example of state constraints

P. Lions, 1986 .

Viscosity Solutions of Hamilton-Jacobi Equations in Banach Spaces

P. Lions, M. Crandall, 1985 .

Some Recent Results in the Optimal Control of Diffusion Processes

P. Lions, 1984 .

Optimal stochastic control of diffusion type processes and Hamilton-Jacobi-Bellman equations

P. Lions, 1982 .

Strategic advantages in mean field games with a major player

Charles Bertucci, Jean-Michel Lasry, Pierre-Louis Lions, 2020, 2002.07034.

Some remarks on Hartree equation

P. Lions, 1981 .

On a free boundary barotropic model

Pierre-Louis Lions, Nader Masmoudi, P. Lions, 1999 .

Axiomes et 'equations fondamentales du traitement d''images

Luis Alvarez, F. Guichard, Pierre-Louis Lions, 1992 .

Appendix to “ The Dynamics of Inequality ”

P. Lions, Benjamin Moll, J. Lasry, 2016 .

Quadratic growth of solutions of fully nonlinear second order equations in $\mathbb{R}^n$

Pierre-Louis Lions, Michael G. Crandall, P. Lions, 1990, Differential and Integral Equations.

Eikonal equations and pathwise solutions to fully non-linear SPDEs

Panagiotis E. Souganidis, Pierre-Louis Lions, Peter K. Friz, 2016, Stochastics and Partial Differential Equations: Analysis and Computations.

Tony F. Chan, Thomas Y. Hou, P. Lions, 1991 .

A Liouville theorem for nonlinear elliptic systems with isotropic nonlinearities

P. Lions, J. Necas, I. Netuka, 1982 .

Contributions to nonlinear partial differential equations

P. Lions, C. Bardos, J. I. Díaz, 1987 .

E . 1 Motivating Facts : the Evolution of Top Wealth Inequality

August, P. Lions, Benjamin Moll, 2016 .

Hamilton-Jacobi Equations and State-Constraints Problems

P. Lions, I. Capuzzo-Dolcetta, 1987 .

On Some Challenging Problems in Nonlinear Partial Differential Equations

P. Lions, 2000 .

Solutions globales d'équations du type Vlasov-Poisson

P. Lions, R. Perna, 1988 .

Remarks on the Existence and Uniqueness of Unbounded Viscosity Solutions of Hamilton-Jacobi Equations.

Pierre-Louis Lions, Michael G. Crandall, P. Lions, 1987 .

Differential games and directional derivatives of viscosity solutions of Issacs' equations II

P. Souganidis, P. Lions, P L Lions, 1986 .

Viscosity solutions and applications : lectures given at the 2nd session of the Centro internazionale matematico estivo (C.I.M.E.) held in Montecatini Terme, Italy, June 12-20, 1995

Centro internazionale matematico estivo. Session, Panagiotis E. Souganidis, Pierre-Louis Lions, 1997 .

Viscosity Solutions of Fully Nonlinear Stochastic Partial Differential Equatios (微分方程式の粘性解とその周辺研究集会報告集)

P. Souganidis, P. Lions, 2002 .

Towards a self-consistent theory of volatility

P. Lions, J. Lasry, 2006 .

Instantaneous self-fulfilling of long-term prophecies on the probabilistic distribution of financial asset values

P. Lions, J. Lasry, 2007 .

Large investor trading impacts on volatility

Pierre-Louis Lions, Jean-Michel Lasry, P. Lions, 2007 .

Fully nonlinear stochastic PDE with semilinear stochastic dependence

Panagiotis E. Souganidis, Pierre-Louis Lions, P. Souganidis, 2000 .

A Characterization of the Existence of Solutions for Hamilton—Jacobi Equations in Ergodic Control Problems with Applications

Hitoshi Ishii, Pierre-Louis Lions, P. Lions, 2000 .

A Strengthened Central Limit Theorem for Smooth Densities

Pierre-Louis Lions, G. Toscani, P. Lions, 1995 .

OPEN PROBLEM: Molecular simulation and related topics: some open mathematical problems

P. Lions, É. Cancès, C. LeBris, 2008 .