We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

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.


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.
Download PDF
Publisher Web site:
Publisher statement:© 2018 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
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

Save or Share this output

Look up in GoogleScholar