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2015 | OriginalPaper | Chapter

Regularity for Mean-Field Games Systems with Initial-Initial Boundary Conditions: The Subquadratic Case

Authors : Diogo A. Gomes, Edgard A. Pimentel

Published in: Dynamics, Games and Science

Publisher: Springer International Publishing

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Abstract

In the present paper, we study forward-forward mean-field games with a power dependence on the measure and subquadratic Hamiltonians. These problems arise in the numerical approximation of stationary mean-field games. We prove the existence of smooth solutions under dimension and growth conditions for the Hamiltonian. To obtain the main result, we combine Sobolev regularity for solutions of the Hamilton-Jacobi equation (using Gagliardo-Nirenberg interpolation) with estimates of polynomial type for solutions of the Fokker-Planck equation.

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Metadata
Title
Regularity for Mean-Field Games Systems with Initial-Initial Boundary Conditions: The Subquadratic Case
Authors
Diogo A. Gomes
Edgard A. Pimentel
Copyright Year
2015
Book
Dynamics, Games and Science

Print ISBN: 978-3-319-16117-4

Electronic ISBN: 978-3-319-16118-1

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-16118-1_15

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