KAUST DepartmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Preprint Posting Date2013-10-17
Online Publication Date2014-10-14
Print Publication Date2015-01-02
Permanent link to this recordhttp://hdl.handle.net/10754/563799
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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.
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
SponsorsD. 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.
PublisherInforma UK Limited