Accepted Paper

Inserted: 3 apr 2020
Last Updated: 18 oct 2021

Journal: Comm. Pure Appl. Math.
Year: 2021

Abstract:

This manuscript constructs global in time solutions to the $master\ equations$ for potential Mean Field Games. The study concerns a class of Lagrangians and initial data functions, which are $displacement\ convex$ 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.

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