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Time dependent mean-field games in the subquadratic case

Bibliography:

D. Gomes H. Sanchez-Morgado and E. Pimentel, Time dependent mean-field games in the subquadratic case. Comm. Partial Differential Equations 40 (2015), no. 1, 40–76.

Authors:

D. Gomes, E. Pimentel, H. Sanchez-Morgado

Keywords:

Mean-field games, Classical solutions, a-priori estimates

Year:

2015

Abstract:

In this paper we consider time-dependent mean-fi eld 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.
 

ISSN:

2015