Time-Dependent Mean-Field Games in the Subquadratic Case
dc.contributor.author | Gomes, Diogo A. | |
dc.contributor.author | Pimentel, Edgard A. | |
dc.contributor.author | Sánchez-Morgado, Héector | |
dc.date.accessioned | 2015-08-03T12:10:31Z | |
dc.date.available | 2015-08-03T12:10:31Z | |
dc.date.issued | 2014-10-14 | |
dc.identifier.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:10.1080/03605302.2014.903574 | |
dc.identifier.issn | 03605302 | |
dc.identifier.doi | 10.1080/03605302.2014.903574 | |
dc.identifier.uri | http://hdl.handle.net/10754/563799 | |
dc.description.abstract | 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. | |
dc.description.sponsorship | 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. | |
dc.publisher | Informa UK Limited | |
dc.relation.url | http://arxiv.org/abs/arXiv:1310.4766v2 | |
dc.subject | A priori estimates | |
dc.subject | Classical solutions | |
dc.subject | Mean-field games | |
dc.title | Time-Dependent Mean-Field Games in the Subquadratic Case | |
dc.type | Article | |
dc.contributor.department | Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ) | |
dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | |
dc.contributor.department | Applied Mathematics and Computational Science Program | |
dc.identifier.journal | Communications in Partial Differential Equations | |
dc.contributor.institution | Instiuto Nacional de Matemática Pura e Aplicada, IMPARio de Janeiro, Brazil | |
dc.contributor.institution | Instituto de Matemáticas, Universidad Nacional Autónoma de MéxicoMexico DF, Mexico | |
dc.identifier.arxivid | 1310.4766 | |
kaust.person | Gomes, Diogo A. | |
dc.date.published-online | 2014-10-14 | |
dc.date.published-print | 2015-01-02 | |
dc.date.posted | 2013-10-17 |
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