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 C1,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. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

C^{1,α} regularity for stationary mean-field games with logarithmic coupling

giuseppe di fazio
Primo
Membro del Collaboration Group
;
2024-01-01

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 C1,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. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.
2024
Regularity, Elliptic equations, Mean Field Games
File in questo prodotto:
File Dimensione Formato  
C1alpha_Tigran_Giuseppe_Diogo.pdf

solo gestori archivio

Tipologia: Versione Editoriale (PDF)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 432.89 kB
Formato Adobe PDF
432.89 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/636249
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact