Weak Solutions of Mean Field Game Master Equations
Speaker:
Jianfeng Zhang, Professor, Department of Mathematics, University of Southern California
Description:
In this talk we consider master equations arising from mean field game problems, under the Lasry-Lions monotonicity condition. Classical solutions of such equations typically require very strong technical conditions. Moreover, unlike the equations arising from mean field control problems, the mean field game master equations are non-local and even classical solutions often do not satisfy the comparison principle, so the standard viscosity solution approach seems infeasible. We shall propose a new notion of weak solutions for such equations and establish its wellposedness. For the crucial regularity in terms of the measures, we construct a smooth mollifier for functions on Wasserstein space, which is new in the literature and is interesting in its own right. The talk is based on a joint work with Chenchen Mou.