H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 102 Citations 68,167 224 World Ranking 12 National Ranking 1

Research.com Recognitions

Awards & Achievements

2008 - Fellow, The World Academy of Sciences

1995 - Member of Academia Europaea

1994 - Academie des sciences, France

1994 - Fields Medal of International Mathematical Union (IMU) ... Such nonlinear partial differential equation simply do not have smooth or even C1 solutions existing after short times. ... The only option is therefore to search for some kind of weak solution. This undertaking is in effect to figure out how to allow for certain kinds of physically correct singularities and how to forbid others. ... Lions and Crandall at last broke open the problem by focusing attention on viscosity solutions, which are defined in terms of certain inequalities holding wherever the graph of the solution is touched on one side or the other by a smooth test function.

1992 - Ampère Prize (Prix Ampère de l’Électricité de France), French Academy of Sciences

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Quantum mechanics
  • Partial differential equation

Mathematical analysis, Nonlinear system, Uniqueness, Partial differential equation and Applied mathematics are his primary areas of study. His Nonlinear system study incorporates themes from Mathematical physics, Schrödinger equation, Type, Complex system and Hartree–Fock method. He interconnects Scalar field and Classical mechanics in the investigation of issues within Complex system.

His Uniqueness research incorporates themes from Image processing, Stochastic control, Optimal control and Poisson's equation. His research integrates issues of Galilean invariance, Elliptic curve and Viscosity solution in his study of Partial differential equation. His Applied mathematics research integrates issues from Weak formulation, Work, Renormalization and Schauder estimates.

His most cited work include:

  • User’s guide to viscosity solutions of second order partial differential equations (4230 citations)
  • Viscosity solutions of Hamilton-Jacobi equations (2199 citations)
  • Image selective smoothing and edge detection by nonlinear diffusion. II (2116 citations)

What are the main themes of his work throughout his whole career to date?

His primary areas of investigation include Mathematical analysis, Partial differential equation, Applied mathematics, Nonlinear system and Uniqueness. His research combines Pure mathematics and Mathematical analysis. His Partial differential equation research includes elements of Boundary value problem, Stochastic control, Optimal control and Existence theorem.

His Applied mathematics research incorporates elements of Multiplicative function, Conservation law and Regular polygon. The various areas that Pierre-Louis Lions examines in his Nonlinear system study include Complex system and Degenerate energy levels. Many of his studies involve connections with topics such as Bounded function and Hamilton–Jacobi equation.

He most often published in these fields:

  • Mathematical analysis (51.77%)
  • Partial differential equation (27.01%)
  • Applied mathematics (22.83%)

What were the highlights of his more recent work (between 2016-2021)?

  • Applied mathematics (22.83%)
  • Mathematical analysis (51.77%)
  • Mean field theory (6.43%)

In recent papers he was focusing on the following fields of study:

His main research concerns Applied mathematics, Mathematical analysis, Mean field theory, Master equation and Mathematical economics. His Applied mathematics study combines topics from a wide range of disciplines, such as Quadratic equation, Partial differential equation, Boundary value problem and Convexity. The study incorporates disciplines such as Nonlinear system and Advection in addition to Mathematical analysis.

His Mean field theory research includes themes of Viscosity, Game theory and Calculus. The Master equation study combines topics in areas such as Structure and Uniqueness. His Mathematical economics research is multidisciplinary, relying on both Simple and Closed loop.

Between 2016 and 2021, his most popular works were:

  • The Master Equation and the Convergence Problem in Mean Field Games (170 citations)
  • The Master Equation and the Convergence Problem in Mean Field Games: (AMS-201) (29 citations)
  • Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach (26 citations)

In his most recent research, the most cited papers focused on:

  • Quantum mechanics
  • Mathematical analysis
  • Geometry

His primary areas of study are Partial differential equation, Mean field theory, Mathematical analysis, Applied mathematics and Master equation. His Partial differential equation research is multidisciplinary, incorporating elements of Simple, Mathematical economics, Consumption and Special case. His research in Mean field theory intersects with topics in Group, System of linear equations, Algebra and Calculus.

His Mathematical analysis study often links to related topics such as Almost surely. Pierre-Louis Lions combines subjects such as Mathematical proof, Work, Type and Convexity with his study of Applied mathematics. His studies deal with areas such as Fokker–Planck equation, Differential equation, Stochastic differential equation, Differential game and Order of accuracy as well as Master equation.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Top Publications

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

Michael G. Crandall;Hitoshi Ishii;Pierre Louis Lions.
Bulletin of the American Mathematical Society (1992)

5319 Citations

Viscosity solutions of Hamilton-Jacobi equations

Michael G. Crandall;Pierre-Louis Lions.
Transactions of the American Mathematical Society (1983)

3219 Citations

Nonlinear scalar field equations, I existence of a ground state

Henri Berestycki;Henri Berestycki;Pierre-Louis Lions;Pierre-Louis Lions.
Archive for Rational Mechanics and Analysis (1983)

2585 Citations

The concentration-compactness principle in the calculus of variations. The locally compact case, part 1

P.L. Lions.
Annales De L Institut Henri Poincare-analyse Non Lineaire (1984)

2553 Citations

Image selective smoothing and edge detection by nonlinear diffusion. II

Luis Alvarez;Pierre-Louis Lions;Jean-Michel Morel.
SIAM Journal on Numerical Analysis (1992)

2413 Citations

The Concentration-Compactness Principle in the Calculus of Variations. (The limit case, Part I.)

Pierre-Louis Lions.
Revista Matematica Iberoamericana (1985)

2345 Citations

Ordinary differential equations, transport theory and Sobolev spaces.

R. J. DiPerna;P. L. Lions.
Inventiones Mathematicae (1989)

2340 Citations

Image recovery via total variation minimization and related problems

Antonin Chambolle;Pierre-Louis Lions.
Numerische Mathematik (1997)

1763 Citations

Mean field games

Jean-Michel Lasry;Pierre Louis Lions;Pierre Louis Lions.
Japanese Journal of Mathematics (2007)

1718 Citations

Generalized Solutions of Hamilton-Jacobi Equations

P. L. Lions.
(1982)

1671 Citations

Profile was last updated on December 6th, 2021.
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The ranking h-index is inferred from publications deemed to belong to the considered discipline.

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