Wilfrid Gangbo : Existence of a solution to an equation arising from Mean Field Games

Posted by Ryan Martin , part of the Departmental Colloquium.

At

Nov. 7, 2014, 3 p.m.

In

SEO 636

Abstract

We construct a small time strong solution to a nonlocal Hamilton-Jacobi equation introduced by Lions, the so-called master equation, originating from the theory of Mean Field Games. We discover a link between metric viscosity solutions to local Hamilton-Jacobi equations studied independently by Ambrosio-Feng and G-Swiech, and the master equation. As a consequence we recover the existence of solutions to the First Order Mean Field Games equations, first proved by Lions. We make a more rigorous connection between the master equation and the Mean Field Games equations. (This talk is based on a joint work with A. Swiech).