Calculus of Variations and Geometric Measure Theory
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A. R. Mészáros - F. J. Silva

On the variational formulation of some stationary second order mean field games systems

created by mészáros on 17 Apr 2017
modified on 14 Nov 2017


Accepted Paper

Inserted: 17 apr 2017
Last Updated: 14 nov 2017

Journal: SIAM J. Math. Anal.
Year: 2017


We consider the variational approach to prove the existence of solutions of second order stationary Mean Field Games 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 from '15. Furthermore, our approach can be used to obtain solutions of systems with multiple populations.


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