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• W224423923 abstract "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." @default.
• W224423923 created "2016-06-24" @default.
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• W224423923 date "2014-10-25" @default.
• W224423923 modified "2023-10-06" @default.
• W224423923 title "Obstacle Mean-Field Game Problem" @default.
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