C1,α regularity for stationary mean-field games with logarithmic coupling

This paper investigates stationary mean-field games (MFGs) on the torus with Lipschitz non-homogeneous diffusion and logarithmic-like couplings. The primary objective is to understand the existence of C 1 , α solutions to address the research gap between low-regularity results for bounded and measur...

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Bibliographic Details
Published in:Nonlinear differential equations and applications 2024, Vol.31 (5)
Main Authors: Bakaryan, Tigran, Di Fazio, Giuseppe, Gomes, Diogo A.
Format: Article
Language:English
Subjects:
Analysis
Couplings
Games
Logarithms
Mathematics
Mathematics and Statistics
Regularity
Toruses
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Summary:This paper investigates stationary mean-field games (MFGs) on the torus with Lipschitz non-homogeneous diffusion and logarithmic-like couplings. The primary objective is to understand the existence of C 1 , α solutions to address the research gap between low-regularity results for bounded and measurable diffusions and the smooth results modeled by the Laplacian. We use the Hopf-Cole transformation to convert the MFG system into a scalar elliptic equation. Then, we apply Morrey space methods to establish the existence and regularity of solutions. The introduction of Morrey space methods offers a novel approach to address regularity issues in the context of MFGs.
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-024-00976-x