Calculus of Variations and Geometric Measure Theory

A. Cesaroni - M. Cirant - S. Dipierro - M. Novaga - E. Valdinoci

On stationary fractional Mean Field Games

created by cesaroni on 29 May 2017
modified by novaga on 16 Jan 2019


Published Paper

Inserted: 29 may 2017
Last Updated: 16 jan 2019

Journal: J. Math. Pures Appl.
Volume: 122
Pages: 1-22
Year: 2019


We provide an existence result for stationary fractional mean field game systems, with fractional exponent greater than $1/2$. In the case in which the coupling is a nonlocal regularizing potential, we obtain existence of solutions under general assumptions on the Hamiltonian. In the case of local coupling, we restrict to the subcritical regime, that is the case in which the diffusion part of the operator dominates the Hamiltonian term. We consider both the case of local bounded coupling and of local unbounded coupling with power-type growth. In this second regime, we impose some conditions on the growth of the coupling and on the growth of the Hamiltonian with respect to the gradient term.