Mean Field Games with state constraints: from mild to pointwise solutions of the PDE system

Piermarco Cannarsa (DIPMAT); Pierre Cardaliaguet (CEREMADE); Rossana Capuani

Mean Field Games with state constraints: from mild to pointwise solutions of the PDE system

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arxiv 1812.11374 v1 pith:4CBYQRMU submitted 2018-12-29 math.OC math.AP

Piermarco Cannarsa (DIPMAT) , Rossana Capuani , Pierre Cardaliaguet (CEREMADE) This is my paper · ORCID

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Mean Field Games with state constraints are differential games with infinitely many agents, each agent facing a constraint on his state. The aim of this paper is to provide a meaning of the PDE system associated with these games, the so-called Mean Field Game system with state constraints. For this, we show a global semiconvavity property of the value function associated with optimal control problems with state constraints.

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Deterministic mean field games with control on the acceleration
math.AP 2019-08 accept novelty 8.0 of 10

For mean field games with double-integrator dynamics, existence of weak solutions and a flow representation of the population density are proved despite a non-coercive Hamiltonian.

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