Existence of weak solutions to first-order stationary mean-field games with dirichlet conditions

Rita Ferreira, Diogo A. Gomes, Teruo Tada

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In 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.
Original languageEnglish (US)
Pages (from-to)4713-4731
Number of pages19
JournalProceedings of the American Mathematical Society
Volume147
Issue number11
DOIs
StatePublished - Jul 24 2019

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