Convergence of the solutions of the MFG discounted Hamilton-Jacobi equation

Abstract

We consider the solution ${\mathcal{V}}_{\delta }$ of the discounted Hamilton-Jacobi equation in the Wasserstein space arising from potential MFG and we prove its full convergence to a corrector function ${\chi }_0$. We follow the structure of the proof of the analogue result in the finite dimensional setting provided by Davini, Fathi, Iturriaga, Zavidovique in 2017. We characterize the limit ${\chi }_0$ through a particular set of smooth Mather measures. A major point that distinguishes the techniques deployed in the standard setting from the ones that we use here is the lack of mollification in the Wasserstain space.

Cited by in corpus (1)

• On weak solutions to first-order discount mean field games