# Seminario di equazioni differenziali e applicazioni: “On the existence and uniqueness of solutions to time-dependent fractional MFG”

## Mercoledì 26 Settembre 2018, ore 12:15 - Sala Riunioni VII Piano - Alessandro Goffi

ARGOMENTI: Seminars

Mercoledì 26 Settembre 2018 alle ore 12:15 in Sala Riunioni VII Piano, Alessandro Goffi (GSSI, L'Aquila)
terrà un seminario dal titolo “On the existence and uniqueness of solutions to time-dependent fractional MFG”.

Abstract
In this joint work with M. Cirant, we establish existence and uniqueness of solutions to evolutive fractional Mean Field Game systems with regularizing coupling, for any order of the fractional laplacian $s\in(0,1)$. 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 $s\leq 1/2$ 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.