Vol. 12, No. 3, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 8, 1861–2108
Issue 7, 1617–1859
Issue 6, 1375–1616
Issue 5, 1131–1373
Issue 4, 891–1130
Issue 3, 567–890
Issue 2, 273–566
Issue 1, 1–272

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Concentration of ground states in stationary mean-field games systems

Annalisa Cesaroni and Marco Cirant

Vol. 12 (2019), No. 3, 737–787

We provide the existence of classical solutions to stationary mean-field game systems in the whole space N , with coercive potential and aggregating local coupling, under general conditions on the Hamiltonian. The only structural assumption we make is on the growth at infinity of the coupling term in terms of the growth of the Hamiltonian. This result is obtained using a variational approach based on the analysis of the nonconvex energy associated to the system. Finally, we show that in the vanishing viscosity limit, mass concentrates around the flattest minima of the potential. We also describe the asymptotic shape of the rescaled solutions in the vanishing viscosity limit, in particular proving the existence of ground states, i.e., classical solutions to mean-field game systems in the whole space without potential, and with aggregating coupling.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

ergodic mean-field games, semiclassical limit, concentration-compactness method, mass concentration, elliptic systems, variational methods
Mathematical Subject Classification 2010
Primary: 35J50
Secondary: 49N70, 35J47, 91A13, 35B25
Received: 16 August 2017
Revised: 25 May 2018
Accepted: 29 June 2018
Published: 7 October 2018
Annalisa Cesaroni
Dipartimento di Scienze Statistiche
Università di Padova
Marco Cirant
Dipartimento di Matematica “Tullio Levi-Civita”
Università di Padova