1King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia 2Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
Interfaces and free boundaries, Tome 17 (2015) no. 1, pp. 55-68
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.
1
King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
2
Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
Diogo A. Gomes; Stefania Patrizi. Obstacle mean-field game problem. Interfaces and free boundaries, Tome 17 (2015) no. 1, pp. 55-68. doi: 10.4171/ifb/333
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title = {Obstacle mean-field game problem},
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