Gradient estimate of HJB and its applications in Graphon Mean Field Game

The Graphon Mean Field Game equations consist of a collection of parameterized Hamilton-Jacobi-Bellman equations, and a collection of parameterized Fokker-Planck-Kolmogorov equations coupled through a given graphon. In this talk, we will discuss the sensitivity of the gradient of HJB solutions with respect to the coefficients, which can be used for the solvability of Graphon Mean Field Game equation. It's based on the joint work with Peter Caines, Daniel Ho, Minyi Huang, and Jiamin Jian, see https://arxiv.org/pdf/2009.12144.pdf.