Global well-posedness of Master equations for deterministic displacement convex potential mean field games

Abstract

This manuscript constructs global in time solutions to the $masterequations$ for potential Mean Field Games. The study concerns a class of Lagrangians and initial data functions, which are $displacementconvex$ and so, it may be in dichotomy with the class of so--called $monotone$ functions, widely considered in the literature. We construct solutions to both the scalar and vectorial master equations in potential Mean Field Games, when the underlying space is the whole space ${\mathbb{R}}^d$ and so, it is not compact.

some sections rearranged, presentation improved, references updated; to appear in Comm. Pure Appl. Math

Cited by in corpus (1)

• Hamilton--Jacobi equations for controlled gradient flows: the comparison principle