Local regularity for mean-field games in the whole space

Diogo A. Gomes, Edgard Pimentel

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We investigate the Sobolev regularity for mean-field games in the whole space Rd. This is achieved by combining integrability for the solutions of the Fokker-Planck equation with estimates for the Hamilton-Jacobi equation in Sobolev spaces. To avoid the mathematical chal- lenges due to the lack of compactness, we prove an entropy dissipation estimate for the adjoint variable. This, together with the non-linear adjoint method, yields uniform estimates for solutions of the Hamilton-Jacobi equation in Wloc1,p (Rd).

Original languageEnglish (US)
Pages (from-to)65-82
Number of pages18
JournalMinimax Theory and its Applications
Issue number1
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© Heldermann Verlag.

ASJC Scopus subject areas

  • Analysis
  • Control and Optimization
  • Computational Mathematics


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