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

Cannarsa, Piermarco; Capuani, Rossana; Cardaliaguet, Pierre (2021), Mean Field Games with state constraints: from mild to pointwise solutions of the PDE system, Calculus of Variations and Partial Differential Equations, 60, 108, p. 1-32. 10.1007/s00526-021-01936-4

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Type
Article accepté pour publication ou publié
Date
2021
Journal name
Calculus of Variations and Partial Differential Equations
Volume
60
Number
108
Publisher
Springer
Pages
1-32
Publication identifier
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Author(s)
Cannarsa, Piermarco
Dipartimento di Matematica [Roma II] [DIPMAT]
Capuani, Rossana
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dipartimento di Matematica [Roma II] [DIPMAT]
Cardaliaguet, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.
Subjects / Keywords
semiconcave functions; state constraints; mean field games; viscosity solutions