Time-Dependent Mean-Field Games in the Subquadratic Case

Diogo A. Gomes, Edgard A. Pimentel, Héector Sánchez-Morgado

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54 Scopus citations


In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension. This is done by combining regularity estimates for the Hamilton-Jacobi equation based on the Gagliardo-Nirenberg interpolation inequality with polynomial estimates for the Fokker-Planck equation. This technique improves substantially the previous results on the regularity of time-dependent mean-field games.
Original languageEnglish (US)
Pages (from-to)40-76
Number of pages37
JournalCommunications in Partial Differential Equations
Issue number1
StatePublished - Oct 14 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: D. Gomes was partially supported by CAMGSD-LARSys through FCT-Portugal and by grants PTDC/MAT-CAL/0749/2012, UTA-CMU/MAT/0007/2009 PTDC/MAT/114397/2009, and UTAustin/MAT/0057/2008. E. Pimentel was supported by CNPq-Brazil, grant GDE/238040/2012-7.

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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