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Article Dans Une Revue Journal of Differential Equations Année : 2020

Non-coercive first order Mean Field Games

Résumé

We study first order evolutive Mean Field Games where the Hamiltonian is non-coercive. This situation occurs, for instance, when some directions are "forbidden" to the generic player at some points. We establish the existence of a weak solution of the system via a vanishing viscosity method and, mainly, we prove that the evolution of the population's density is the push-forward of the initial density through the flow characterized almost everywhere by the optimal trajectories of the control problem underlying the Hamilton-Jacobi equation. As preliminary steps, we need that the optimal trajectories for the control problem are unique (at least for a.e. starting points) and that the optimal controls can be expressed in terms of the horizontal gradient of the value function.
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Dates et versions

hal-01938798 , version 1 (29-11-2018)

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Paola Mannucci, Claudio Marchi, Carlo Mariconda, Nicoletta Tchou. Non-coercive first order Mean Field Games. Journal of Differential Equations, 2020, 269 (5), pp.4503-4543. ⟨10.1016/j.jde.2020.03.035⟩. ⟨hal-01938798⟩
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