Title: Weak Solutions of Mean Field Game Master Equations.

Abstract: In this talk we study master equations arising from
mean field game problems, under the crucial monotonicity conditions.
Classical solutions of such equations require very strong technical
conditions. Moreover, unlike the master equations arising from mean
field control problems, the mean field game master equations are
non-local and even classical solutions typically do not satisfy the
comparison principle, so the standard viscosity solution approach seems
infeasible. We shall propose a notion of weak solution for such
equations and establish its wellposedness. Our approach relies on a new
smooth mollifier for functions of measures, which unfortunately does not
keep the monotonicity property, and the stability result of master
equations. The talk is based on a joint work with Jianfeng Zhang.