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

Diogo A. Gomes, Edgard A. Pimentel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.
Original languageEnglish (US)
Title of host publicationCIM Series in Mathematical Sciences
PublisherSpringer Nature
Pages291-304
Number of pages14
ISBN (Print)9783319161174
DOIs
StatePublished - 2015

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