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. - STAMPA. - 51:(2019), pp. 913-954. [10.1137/18M1216420]
On the existence and uniqueness of solutions to time-dependent fractional MFG
Goffi A.
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.File | Dimensione | Formato | |
---|---|---|---|
18m1216420.pdf
Accesso chiuso
Tipologia:
Pdf editoriale (Version of record)
Licenza:
Tutti i diritti riservati
Dimensione
609.94 kB
Formato
Adobe PDF
|
609.94 kB | Adobe PDF | Richiedi una copia |
1809.03034v2.pdf
accesso aperto
Tipologia:
Versione finale referata (Postprint, Accepted manuscript)
Licenza:
Open Access
Dimensione
519.69 kB
Formato
Adobe PDF
|
519.69 kB | Adobe PDF |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.