We establish existence and uniqueness of solutions to evolutive fractional mean field game systems with regularizing coupling for any order of the fractional Laplacian s ∈ (0,1). The existence is addressed via the vanishing viscosity method. In particular, we prove that in the subcritical regime s > 1/2 the solution of the system is classical, while if s ≤ 1/2, we find a distributional energy solution. To this aim, we develop an appropriate functional setting based on parabolic Bessel potential spaces. We show uniqueness of solutions both under monotonicity conditions and for short time horizons.

On the existence and uniqueness of solutions to time-dependent fractional MFG / Cirant, M.; Goffi, A.. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 51:2(2019), pp. 913-954. [10.1137/18M1216420]

On the existence and uniqueness of solutions to time-dependent fractional MFG

Cirant M.;
2019

Abstract

We establish existence and uniqueness of solutions to evolutive fractional mean field game systems with regularizing coupling for any order of the fractional Laplacian s ∈ (0,1). The existence is addressed via the vanishing viscosity method. In particular, we prove that in the subcritical regime s > 1/2 the solution of the system is classical, while if s ≤ 1/2, we find a distributional energy solution. To this aim, we develop an appropriate functional setting based on parabolic Bessel potential spaces. We show uniqueness of solutions both under monotonicity conditions and for short time horizons.
On the existence and uniqueness of solutions to time-dependent fractional MFG / Cirant, M.; Goffi, A.. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 51:2(2019), pp. 913-954. [10.1137/18M1216420]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2861483
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