Obstacle mean-field game problem | Zendy

Diogo A. Gomes | Zendy; Stefania Patrizi | Zendy

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Obstacle mean-field game problem

Author(s) -

Diogo A. Gomes,

Stefania Patrizi

Publication year - 2015

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/333

Subject(s) - obstacle , uniqueness , mathematics , differentiable function , limit (mathematics) , logarithm , operator (biology) , obstacle problem , measure (data warehouse) , field (mathematics) , mathematical optimization , mathematical analysis , computer science , pure mathematics , variational inequality , biochemistry , chemistry , repressor , database , political science , transcription factor , law , gene

In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions. © European Mathematical Society 2015

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