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- W2617100196 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. Nous prouvons un résultat d'existence pour des systèmes de jeux à champ moyen stationnaires et fractionnaires, avec un exposant fractionnaire supérieur à 1/2. Dans le cas où le couplage est un potentiel de régularisation non local, nous obtenons l'existence de solutions sous des hypothèses générales sur l'hamiltonien. Dans le cas où le couplage est local, nous considérons le régime sous-critique, c'est le cas dans lequel la partie de diffusion de l'opérateur domine le terme hamiltonien. Nous considérons à la fois le cas du couplage limité local et du couplage local non borné avec la croissance du type puissance. Dans ce second régime, nous imposons certaines conditions sur la croissance du couplage et sur la croissance de l'hamiltonien par rapport au terme gradient." @default.
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- W2617100196 date "2019-02-01" @default.
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- W2617100196 title "On stationary fractional mean field games" @default.
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- W2617100196 doi "https://doi.org/10.1016/j.matpur.2017.10.013" @default.
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