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dc.contributor.authorGomes, Diogo A.
dc.contributor.authorPimentel, Edgard A.
dc.contributor.authorSánchez-Morgado, Héector
dc.date.accessioned2015-08-03T12:10:31Z
dc.date.available2015-08-03T12:10:31Z
dc.date.issued2014-10-14
dc.identifier.citationGomes, D. A., Pimentel, E. A., & Sánchez-Morgado, H. (2014). Time-Dependent Mean-Field Games in the Subquadratic Case. Communications in Partial Differential Equations, 40(1), 40–76. doi:10.1080/03605302.2014.903574
dc.identifier.issn03605302
dc.identifier.doi10.1080/03605302.2014.903574
dc.identifier.urihttp://hdl.handle.net/10754/563799
dc.description.abstractIn 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.
dc.description.sponsorshipD. 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.
dc.publisherInforma UK Limited
dc.relation.urlhttp://arxiv.org/abs/arXiv:1310.4766v2
dc.subjectA priori estimates
dc.subjectClassical solutions
dc.subjectMean-field games
dc.titleTime-Dependent Mean-Field Games in the Subquadratic Case
dc.typeArticle
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalCommunications in Partial Differential Equations
dc.contributor.institutionInstiuto Nacional de Matemática Pura e Aplicada, IMPARio de Janeiro, Brazil
dc.contributor.institutionInstituto de Matemáticas, Universidad Nacional Autónoma de MéxicoMexico DF, Mexico
dc.identifier.arxivid1310.4766
kaust.personGomes, Diogo A.
dc.date.published-online2014-10-14
dc.date.published-print2015-01-02
dc.date.posted2013-10-17


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