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

Abstract : 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 growth 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 \cite{MesSil}. Furthermore, our approach can be used to obtain solutions of systems with multiple populations.
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Preprints, Working Papers, ...

Cited literature [35 references]

https://hal.inria.fr/hal-01502723
Contributor : Alpár Richárd Mészáros <>
Submitted on : Monday, April 17, 2017 - 2:31:28 AM
Last modification on : Monday, December 14, 2020 - 5:25:15 PM
Long-term archiving on: : Tuesday, July 18, 2017 - 12:18:19 PM

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### Identifiers

• HAL Id : hal-01502723, version 3
• ARXIV : 1704.02125

### Citation

Alpár Richárd Mészáros, Francisco J. Silva. On the variational formulation of some stationary second order mean field games systems. 2017. ⟨hal-01502723v3⟩

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