Time dependent mean-field games in the subquadratic case

by D. Gomes, E. Pimentel, H. Sanchez-Morgado
Manuscripts Year: 2015


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.


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.




Classical solutions a-priori estimates Mean field games