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On the Variational Formulation of Some Stationary Second-Order Mean Field Games Systems

Mészáros, Alpár Richárd; Silva, Francisco J.

On the Variational Formulation of Some Stationary Second-Order Mean Field Games Systems Thumbnail


Authors

Francisco J. Silva



Abstract

We consider the variational approach to prove the existence of solutions of second-order stationary Mean Field Games systems on a bounded domain $\Omega\subseteq {\mathbb R}^{d}$ with Neumann boundary conditions and with and without density constraints. We consider Hamiltonians which grow as $|\cdot|^{q'}$, where $q'=q/(q-1)$ and $q>d$. Despite this restriction, our approach allows us to prove the existence of solutions in the case of rather general coupling terms. When density constraints are taken into account, our results improve those in [A. R. Mészáros and F. J. Silva, J. Math. Pures Appl., 104 (2015), pp. 1135--1159]. Furthermore, our approach can be used to obtain solutions of systems with multiple populations.

Journal Article Type Article
Acceptance Date Oct 30, 2017
Online Publication Date Feb 15, 2018
Publication Date 2018
Deposit Date Oct 1, 2019
Publicly Available Date Feb 28, 2020
Journal SIAM Journal on Mathematical Analysis
Print ISSN 0036-1410
Electronic ISSN 1095-7154
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 50
Issue 1
Pages 1255-1277
DOI https://doi.org/10.1137/17m1125960
Public URL https://durham-repository.worktribe.com/output/1290298
Related Public URLs https://arxiv.org/abs/1704.02125

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© 2018, Society for Industrial and Applied Mathematics.






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