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

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