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

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,...

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 60; no. 3; pp. 1 - 33
Main Authors Cannarsa, Piermarco, Capuani, Rossana, Cardaliaguet, Pierre
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021
Springer Nature B.V
Springer Verlag
Subjects
Analysis
Analysis of PDEs
Calculus of Variations and Optimal Control; Optimization
Control
Differential games
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Optimal control
Optimization and Control
Systems Theory
Theoretical
49N60
49K40
49L25
49N90
semiconcave functions
viscosity solutions MSC Subject classifications: 49L25
mean field games
state constraints
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ISSN0944-2669
1432-0835
DOI10.1007/s00526-021-01936-4

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Summary: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.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-021-01936-4