Mean field games with state constraints: from mild to pointwise solutions of the PDE system

By Piermarco Cannarsa, Rossana Capuani, Pierre Cardaliaguet. Calculus of Variations and Partial Differential Equations, 2018

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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.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/b215b40661c0dbc6b91f629c01a1ecb2cd17f89d