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arXiv · 1310.4766

Time dependent mean-field games in the subquadratic case

Diogo A. Gomes·Edgard Pimentel·Héctor Sánchez-Morgado
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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.

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Diogo A. Gomes, Edgard Pimentel, Héctor Sánchez-Morgado. 2013-11-25. Time dependent mean-field games in the subquadratic case. https://arxiv.org/abs/1310.4766

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