Time-Dependent Mean-Field Games in the Subquadratic Case

Diogo A. Gomes; Edgard A. Pimentel; Héector Sánchez-Morgado

doi:10.1080/03605302.2014.903574

Time-Dependent Mean-Field Games in the Subquadratic Case

Diogo A. Gomes, Edgard A. Pimentel, Héector Sánchez-Morgado

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54 Scopus citations

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.

Original language	English (US)
Pages (from-to)	40-76
Number of pages	37
Journal	Communications in Partial Differential Equations
Volume	40
Issue number	1
DOIs	https://doi.org/10.1080/03605302.2014.903574
State	Published - Oct 14 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/03605302.2014.903574

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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.",

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note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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.",

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AU - Gomes, Diogo A.

AU - Pimentel, Edgard A.

AU - Sánchez-Morgado, Héector

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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.

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N2 - 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.

AB - 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.

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JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

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Time-Dependent Mean-Field Games in the Subquadratic Case

Abstract

Bibliographical note

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