Existence of weak solutions to first-order stationary mean-field games with dirichlet conditions
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
KAUST Grant NumberOSR-CRG2017-3452
Preprint Posting Date2018-04-19
Online Publication Date2019-07-24
Print Publication Date2019-07-30
Permanent link to this recordhttp://hdl.handle.net/10754/627601
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AbstractIn this paper, we study first-order stationary monotone meanfield games (MFGs) with Dirichlet boundary conditions. Whereas Dirichlet conditions may not be satisfied for Hamilton-Jacobi equations, here we establish the existence of solutions to MFGs that satisfy those conditions. To construct these solutions, we introduce a monotone regularized problem. Applying Schaefer's fixed-point theorem and using the monotonicity of the MFG, we verify that there exists a unique weak solution to the regularized problem. Finally, we take the limit of the solutions of the regularized problem and, using Minty's method, we show the existence of weak solutions to the original MFG.
CitationFerreira, R., Gomes, D., & Tada, T. (2019). Existence of weak solutions to first-order stationary mean-field games with Dirichlet conditions. Proceedings of the American Mathematical Society, 147(11), 4713–4731. doi:10.1090/proc/14475
SponsorsThe authors were partially supported by baseline and start-up funds from King Abdullah University of Science and Technology (KAUST) and by KAUST project OSR-CRG2017-3452.
PublisherAmerican Mathematical Society (AMS)