
arXiv: 1410.6942
handle: 10754/594150
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.
ddc:510, article, penalization method, 35J87, mean-field games -- obstacle problem -- penalization method, Mean-field games, Penalization method, 510, mean-field games, Obstacle problem, Mathematics - Analysis of PDEs, obstacle problem, FOS: Mathematics, 49L99, Analysis of PDEs (math.AP)
ddc:510, article, penalization method, 35J87, mean-field games -- obstacle problem -- penalization method, Mean-field games, Penalization method, 510, mean-field games, Obstacle problem, Mathematics - Analysis of PDEs, obstacle problem, FOS: Mathematics, 49L99, Analysis of PDEs (math.AP)
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