P. Lions

Publications313
h-index93
Citations55,177
Highly Influential Citations4,513
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User’s guide to viscosity solutions of second order partial differential equations
The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence…
The concentration-compactness principle in the Calculus of Variations
Mathematical topics in fluid mechanics
Ordinary differential equations, transport theory and Sobolev spaces
SummaryWe obtain some new existence, uniqueness and stability results for ordinary differential equations with coefficients in Sobolev spaces. These results are deduced from corresponding results on…
Image selective smoothing and edge detection by nonlinear diffusion. II
A new version of the Perona and Malik theory for edge detection and image restoration is proposed. This new version keeps all the improvements of the original model and avoids its drawbacks: it is…
Mean field games
Abstract.We survey here some recent studies concerning what we call mean-field models by analogy with Statistical Mechanics and Physics. More precisely, we present three examples of our mean-field…
The concentration-compactness principle in the calculus of variations. The locally compact case
Generalized Solutions of Hamilton-Jacobi Equations
Splitting Algorithms for the Sum of Two Nonlinear Operators
TLDR
This work studies two splitting algorithms for (stationary and evolution) problems involving the sum of two monotone operators with real-time requirements.
Orbital stability of standing waves for some nonlinear Schrödinger equations
We present a general method which enables us to prove the orbital stability of some standing waves in nonlinear Schrödinger equations. For example, we treat the cases of nonlinear Schrödinger…
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