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Article Dans Une Revue Journal of the London Mathematical Society Année : 2019

New estimates on the regularity of the pressure in density-constrained Mean Field Games

Résumé

We consider variational Mean Field Games endowed with a constraint on the maximal density of the distribution of players. Minimizers of the variational formulation are equilibria for a game where both the running cost and the final cost of each player is augmented by a pressure effect, i.e. a positive cost concentrated on the set where the density saturates the constraint. Yet, this pressure is a priori only a measure and regularity is needed to give a precise meaning to its integral on trajectories. We improve, in the limited case where the Hamiltonian is quadratic, which allows to use optimal transport techniques after time-discretization, the results obtained in a paper of the second author with Cardaliaguet and Mészáros. We prove H1 and L infinity regularity under very mild assumptions on the data, and explain the consequences for the MFG, in terms of the value function and of the Lagrangian equilibrium formulation.
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Dates et versions

hal-01930480 , version 1 (22-11-2018)
hal-01930480 , version 2 (13-05-2019)

Identifiants

Citer

Hugo Lavenant, Filippo Santambrogio. New estimates on the regularity of the pressure in density-constrained Mean Field Games. Journal of the London Mathematical Society, In press, ⟨10.1112/jlms.12245⟩. ⟨hal-01930480v2⟩
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