Type
ArticleKAUST Department
Center 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
Date
2014-10-14Preprint Posting Date
2013-10-17Online Publication Date
2014-10-14Print Publication Date
2015-01-02Permanent link to this record
http://hdl.handle.net/10754/563799
Metadata
Show full item recordAbstract
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.Citation
Gomes, 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:10.1080/03605302.2014.903574Sponsors
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.Publisher
Informa UK LimitedarXiv
1310.4766Additional Links
http://arxiv.org/abs/arXiv:1310.4766v2ae974a485f413a2113503eed53cd6c53
10.1080/03605302.2014.903574