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.

On stationary fractional mean field games / Cesaroni, Annalisa; Cirant, Marco; Dipierro, Serena; Novaga, Matteo; Valdinoci, Enrico. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 122:(2019), pp. 1-22. [10.1016/j.matpur.2017.10.013]

On stationary fractional mean field games

Cirant, Marco;
2019-01-01

Abstract

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.
2019
On stationary fractional mean field games / Cesaroni, Annalisa; Cirant, Marco; Dipierro, Serena; Novaga, Matteo; Valdinoci, Enrico. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 122:(2019), pp. 1-22. [10.1016/j.matpur.2017.10.013]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2857482
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