Calculus of Variations and Geometric Measure Theory

M. Cirant - A. Cosenza - G. Verzini

Ergodic Mean Field Games: existence of local minimizers up to the Sobolev critical case

created by cosenza on 29 Mar 2024
modified on 05 Jul 2024


Published Paper

Inserted: 29 mar 2024
Last Updated: 5 jul 2024

Journal: Calc. Var.
Volume: 63
Year: 2024

ArXiv: 2301.11692 PDF


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.