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    Time-Dependent Mean-Field Games in the Subquadratic Case

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    Type
    Article
    Authors
    Gomes, Diogo A. cc
    Pimentel, Edgard A.
    Sánchez-Morgado, Héector
    KAUST 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
    2014-10-14
    Preprint Posting Date
    2013-10-17
    Online Publication Date
    2014-10-14
    Print Publication Date
    2015-01-02
    Permanent link to this record
    http://hdl.handle.net/10754/563799
    
    Metadata
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    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.
    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
    Sponsors
    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 Limited
    Journal
    Communications in Partial Differential Equations
    DOI
    10.1080/03605302.2014.903574
    arXiv
    1310.4766
    Additional Links
    http://arxiv.org/abs/arXiv:1310.4766v2
    ae974a485f413a2113503eed53cd6c53
    10.1080/03605302.2014.903574
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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