12 citations · 45 across the 31 of their papers we have counts for
29 papers · 1 filter
An approximation of the squared Wasserstein distance and an application to Hamilton-Jacobi equations
Charles Bertucci, Pierre Louis Lions
We provide a simple approximation of the squared Wasserstein distance on R^d when one of the two measures is fixed. This approximation converges locally uniformly. More i…
A spectral dominance approach to large random matrices: part II
Charles Bertucci, Jean-Michel Lasry, Pierre Louis Lions
This paper is the second of a series devoted to the study of the dynamics of the spectrum of large random matrices. We study general extensions of the partial differential equation…
A two spaces extension of Cauchy-Lipschitz Theorem
Charles Bertucci, Pierre Louis Lions
We adapt the classical theory of local well-posedness of evolution problems to cases in which the nonlinearity can be accurately quantified by two different norms. For ordinary dif…
A convergence result for a local planning problem for mean field games and rigorous proof of a Freidlin-Ventchel-type Large Deviations Principle for the KPZ equation
Pierre-Louis Lions, Panagiotis E. Souganidis
We prove the convergence of a viscous approximation to an one dimensional local mean field type planning problem with singular initial and terminal measures. Then we use this resul…
Linear and nonlinear transport equations with coordinate-wise increasing velocity fields
Pierre-Louis Lions, Benjamin Seeger
We consider linear and nonlinear transport equations with irregular velocity fields, motivated by models coming from mean field games. The velocity fields are assumed to increase i…
Transport equations and flows with one-sided Lipschitz velocity fields
Pierre-Louis Lions, Benjamin Seeger
We study first- and second-order linear transport equations, as well as ODE and SDE flows, with velocity fields satisfying a one-sided Lipschitz condition. Depending on the time di…