On the existence of classical solutions for stationary extended mean field games

Diogo A. Gomes, Stefania Patrizi, Vardan Voskanyan

Research output: Contribution to journalArticlepeer-review

90 Scopus citations


In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved. © 2013 Elsevier Ltd. All rights reserved.
Original languageEnglish (US)
Pages (from-to)49-79
Number of pages31
JournalNonlinear Analysis: Theory, Methods & Applications
StatePublished - Apr 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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