A-priori estimates for stationary mean-field games

Diogo A. Gomes*, Gabriel E. Pires, Héector Sánchez-Morgado

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


In this paper we establish a new class of a-priori estimates for stationary mean-field games which have a quasi-variational structure. In particular we prove W1,2 estimates for the value function u and that the players distribution m satises √W1,2We discuss further results for powerlike nonlinearities and prove higher regularity if the space dimension is 2. In particular we also obtain in this last case W2,p estimates for u.

Original languageEnglish (US)
Pages (from-to)303-314
Number of pages12
JournalNetworks and Heterogeneous Media
Issue number2
StatePublished - Jun 2012
Externally publishedYes


  • A-priori estimates
  • Mean field games
  • Variational and quasi-variational methods

ASJC Scopus subject areas

  • Statistics and Probability
  • General Engineering
  • Computer Science Applications
  • Applied Mathematics


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