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Mathematics > Analysis of PDEs

arXiv:1804.07175 (math)
[Submitted on 19 Apr 2018]

Title:Existence of weak solutions to first-order stationary mean-field games with Dirichlet conditions

Authors:Rita Ferreira, Diogo Gomes, Teruo Tada
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Abstract:In this paper, we study first-order stationary monotone mean-field games (MFGs) with Dirichlet boundary conditions. While for Hamilton--Jacobi equations Dirichlet conditions may not be satisfied, here, we establish the existence of solutions of 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.
Comments: 15 pages
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.07175 [math.AP]
  (or arXiv:1804.07175v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.07175

Submission history

From: Rita Ferreira [view email]
[v1] Thu, 19 Apr 2018 13:55:32 UTC (20 KB)
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