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Sobolev regularity for first order mean field games.

Jameson Graber, P. and Mészáros, Alpár R. (2018) 'Sobolev regularity for first order mean field games.', Annales de l'Institut Henri Poincaré C, analyse non linéaire., 35 (6). pp. 1557-1576.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.anihpc.2018.01.002
Publisher statement:© 2018 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:23 January 2018
Date deposited:28 February 2020
Date of first online publication:01 February 2018
Date first made open access:28 February 2020

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