Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Existence of weak solutions to first-order stationary mean-field games with Dirichlet conditions
HTML articles powered by AMS MathViewer

by Rita Ferreira, Diogo Gomes and Teruo Tada PDF
Proc. Amer. Math. Soc. 147 (2019), 4713-4731 Request permission

Abstract:

In this paper, we study first-order stationary monotone mean-field 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.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35J56, 35A01
  • Retrieve articles in all journals with MSC (2010): 35J56, 35A01
Additional Information
  • Rita Ferreira
  • Affiliation: King Abdullah University of Science and Technology (KAUST), CEMSE Division, Thuwal 23955-6900, Saudi Arabia
  • MR Author ID: 839299
  • Email: rita.ferreira@kaust.edu.sa
  • Diogo Gomes
  • Affiliation: King Abdullah University of Science and Technology (KAUST), CEMSE Division, Thuwal 23955-6900, Saudi Arabia
  • MR Author ID: 638220
  • Email: diogo.gomes@kaust.edu.sa
  • Teruo Tada
  • Affiliation: King Abdullah University of Science and Technology (KAUST), CEMSE Division, Thuwal 23955-6900, Saudi Arabia
  • Email: teruo.tada@kaust.edu.sa
  • Received by editor(s): May 3, 2018
  • Received by editor(s) in revised form: November 14, 2018
  • Published electronically: July 30, 2019
  • Additional Notes: 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.
  • Communicated by: Catherine Sulem
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4713-4731
  • MSC (2010): Primary 35J56, 35A01
  • DOI: https://doi.org/10.1090/proc/14475
  • MathSciNet review: 4011507