PDE Seminar (2017/7/25): On a Mean Field Game equation

2017-7-25 16:30 - 2017-7-25 18:00
Faculty of Science Building #3, Room 309
Wilfrid Gangbo (University of California, Los Angeles)
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).