Regularity For Stationary Mean-Field Games With Logarithmic Coupling

Abstract
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 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.

Acknowledgements
The authors were supported by King Abdullah University of Science and Technology (KAUST) baseline funds and KAUST OSR-CRG2021-4674

Publisher
arXiv

arXiv
2310.17027

Additional Links
https://arxiv.org/pdf/2310.17027.pdf

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