KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
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AbstractIn 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.
CitationGomes D, Patrizi S (2015) Obstacle mean-field game problem. Interfaces and Free Boundaries 17: 55–68. Available: http://dx.doi.org/10.4171/ifb/333.
SponsorsKAUST, King Abdullah University of Science and Technology
PublisherEuropean Mathematical Publishing House
JournalInterfaces and Free Boundaries