Time dependent mean-field games in the subquadratic case
Analysis of PDEs
2013-11-26 v2
Abstract
In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension. This is done by combining regularity estimates for the Hamilton-Jacobi equation based on the Gagliardo-Nirenberg interpolation inequality with polynomial estimates for the Fokker-Planck equation. This technique improves substantially the previous results on the regularity of time-dependent mean-field games.
Keywords
Cite
@article{arxiv.1310.4766,
title = {Time dependent mean-field games in the subquadratic case},
author = {Diogo A. Gomes and Edgard Pimentel and Héctor Sánchez-Morgado},
journal= {arXiv preprint arXiv:1310.4766},
year = {2013}
}