Sobolev regularity for first order mean field games

Jameson Graber, P.; Mészáros, Alpár R.

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: Feb 28, 2020
• Journal: Annales de l'Institut Henri Poincaré (C) Non Linear Analysis
• Print ISSN: 0294-1449
• Electronic ISSN: 1873-1430
• 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
• Public URL: https://durham-repository.worktribe.com/output/1320018
• Related Public URLs: https://arxiv.org/abs/1708.06190