3 papers
math.AP2024
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…
math.AP2024
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…
math.AP2023
On Lipschitz solutions of mean field games master equations
Charles Bertucci, Jean-Michel Lasry, Pierre-Louis Lions
We develop a theory of existence and uniqueness of solutions of MFG master equations when the initial condition is Lipschitz continuous. Namely, we show that as long as the solutio…