Dr Alpar Meszaros alpar.r.meszaros@durham.ac.uk
Associate Professor
A variational approach to second order mean field games with density constraints: The stationary case
Mészáros, Alpár Richárd; Silva, Francisco J.
Authors
Francisco J. Silva
Abstract
In this paper we study second order stationary Mean Field Game systems under density constraints on a bounded domain . We show the existence of weak solutions for power-like Hamiltonians with arbitrary order of growth. Our strategy is a variational one, i.e. we obtain the Mean Field Game system as the optimality condition of a convex optimization problem, which has a solution. When the Hamiltonian has a growth of order , the solution of the optimization problem is continuous which implies that the problem constraints are qualified. Using this fact and the computation of the subdifferential of a convex functional introduced by Benamou and Brenier (see [1]), we prove the existence of a solution of the MFG system. In the case where the Hamiltonian has a growth of order , the previous arguments do not apply and we prove the existence by means of an approximation argument.
Citation
Mészáros, A. R., & Silva, F. J. (2015). A variational approach to second order mean field games with density constraints: The stationary case. Journal de Mathématiques Pures et Appliquées, 104(6), 1135-1159. https://doi.org/10.1016/j.matpur.2015.07.008
Journal Article Type | Article |
---|---|
Online Publication Date | Jul 1, 2015 |
Publication Date | Dec 1, 2015 |
Deposit Date | Oct 1, 2019 |
Publicly Available Date | Feb 28, 2020 |
Journal | Journal de Mathématiques Pures et Appliquées |
Print ISSN | 0021-7824 |
Electronic ISSN | 1776-3371 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 104 |
Issue | 6 |
Pages | 1135-1159 |
DOI | https://doi.org/10.1016/j.matpur.2015.07.008 |
Public URL | https://durham-repository.worktribe.com/output/1284899 |
Related Public URLs | https://arxiv.org/abs/1502.06026 |
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Copyright Statement
© 2015 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
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