Existence of weak solutions to first-order stationary mean-field games with dirichlet conditions
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FGT_MFG_Dirichlet_final (1).pdf
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ArticleAuthors
Ferreira, Rita
Gomes, Diogo A.

Tada, Teruo
KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionApplied Mathematics and Computational Science Program
KAUST Grant Number
OSR-CRG2017-3452Date
2019-07-24Preprint Posting Date
2018-04-19Online Publication Date
2019-07-24Print Publication Date
2019-07-30Permanent link to this record
http://hdl.handle.net/10754/627601
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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.Citation
Ferreira, 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/14475Sponsors
The 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.Publisher
American Mathematical Society (AMS)arXiv
1804.07175Additional Links
http://www.ams.org/proc/2019-147-11/S0002-9939-2019-14475-0/ae974a485f413a2113503eed53cd6c53
10.1090/proc/14475