Strong solutions for time-dependent mean field games with non-separable Hamiltonians
Abstract
We prove existence theorems for strong solutions of time-dependent mean field games with non-separable Hamiltonian. In a recent announcement, we showed existence of small, strong solutions for mean field games with local coupling. We first generalize that prior work to allow for non-separable Hamiltonians. This proof is inspired by the work of Duchon and Robert on the existence of small-data vortex sheets in incompressible fluid mechanics. Our next existence result is in the case of weak coupling of the system; that is, we allow the data to be of arbitrary size, but instead require that the (still possibly non-separable) Hamiltonian be small in a certain sense. The proof of this theorem relies upon an appeal to the implicit function theorem.
Cite
@article{arxiv.1605.01745,
title = {Strong solutions for time-dependent mean field games with non-separable Hamiltonians},
author = {David M. Ambrose},
journal= {arXiv preprint arXiv:1605.01745},
year = {2016}
}