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

Mészáros, Alpár Richárd; Silva, Francisco J.

doi:10.1137/17m1125960

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

Mészáros, Alpár Richárd; Silva, Francisco J.

Authors

Dr Alpar Meszaros alpar.r.meszaros@durham.ac.uk
Associate Professor

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.

Citation

Mészáros, A. R., & Silva, F. J. (2018). On the Variational Formulation of Some Stationary Second-Order Mean Field Games Systems. SIAM Journal on Mathematical Analysis, 50(1), 1255-1277. https://doi.org/10.1137/17m1125960

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
Related Public URLs	https://arxiv.org/abs/1704.02125