Ergodic mean field games: existence of local minimizers up to the Sobolev critical case

We investigate the existence of solutions to viscous ergodic Mean Field Games systems in bounded domains with Neumann boundary conditions and local, possibly aggregative couplings. In particular we exploit the associated variational structure and search for constrained minimizers of a suitable funct...

Full description

Saved in:
Bibliographic Details
Published in:Calculus of variations and partial differential equations 2024-06, Vol.63 (5), Article 134
Main Authors: Cirant, Marco, Cosenza, Alessandro, Verzini, Gianmaria
Format: Article
Language:English
Subjects:
Analysis
Boundary conditions
Calculus of Variations and Optimal Control
Optimization
Control
Couplings
Ergodic processes
Games
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We investigate the existence of solutions to viscous ergodic Mean Field Games systems in bounded domains with Neumann boundary conditions and local, possibly aggregative couplings. In particular we exploit the associated variational structure and search for constrained minimizers of a suitable functional. Depending on the growth of the coupling, we detect the existence of global minimizers in the mass subcritical and critical case, and of local minimizers in the mass supercritical case, notably up to the Sobolev critical case.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-024-02744-2