Skip to main content

Research Repository

Advanced Search

Sobolev regularity for first order mean field games

Jameson Graber, P.; Mészáros, Alpár R.

Sobolev regularity for first order mean field games Thumbnail


Authors

P. Jameson Graber



Abstract

In this paper we obtain Sobolev estimates for weak solutions of first order variational Mean Field Game systems with coupling terms that are local functions of the density variable. Under some coercivity conditions on the coupling, we obtain first order Sobolev estimates for the density variable, while under similar coercivity conditions on the Hamiltonian we obtain second order Sobolev estimates for the value function. These results are valid both for stationary and time-dependent problems. In the latter case the estimates are fully global in time, thus we resolve a question which was left open in [23]. Our methods apply to a large class of Hamiltonians and coupling functions.

Citation

Jameson Graber, P., & Mészáros, A. R. (2018). Sobolev regularity for first order mean field games. Annales de l'Institut Henri Poincaré C, 35(6), 1557-1576. https://doi.org/10.1016/j.anihpc.2018.01.002

Journal Article Type Article
Acceptance Date Jan 23, 2018
Online Publication Date Feb 1, 2018
Publication Date Sep 30, 2018
Deposit Date Oct 1, 2019
Publicly Available Date Mar 28, 2024
Journal Annales de l'Institut Henri Poincaré (C) Non Linear Analysis
Print ISSN 0294-1449
Publisher EMS Press
Peer Reviewed Peer Reviewed
Volume 35
Issue 6
Pages 1557-1576
DOI https://doi.org/10.1016/j.anihpc.2018.01.002
Related Public URLs https://arxiv.org/abs/1708.06190

Files





You might also like



Downloadable Citations