[Reggio Emilia][Seminario] Simone Creo (Università Roma La Sapienza) 02/07/2025 Ore 14:30

[valentina.taddei]

Mercoledì 2 Luglio alle ore 14.30 presso l'aula F0.2 del Dipartimento di Scienze e Metodi dell'Ingegneria, Padiglione Buccola-Bisi, via Amendola 2, Reggio Emilia

Simone Creo (Università Roma La Sapienza) terrà un seminario dal titolo 

Well-posedness and regularity results for fractional Wentzell-type problems in extension domains

Abstract:

In this talk we will investigate parabolic fractional Wentzell-type problems in domains with irregular boundary, e.g. of fractal type.

We will first consider an autonomous problem for the regional fractional p-Laplacian, coupled with a nonlocal boundary condition. We will prove the existence and uniqueness of the weak solution of the problem via nonlinear semigroup theory, and then we will investigate the regularity of the nonlinear semigroup (namely, its ultracontractivity).

We will then consider the (linear) non-autonomous case, involving time-dependent nonlocal operators acting both in the bulk and on the boundary. Local and global (in time) existence and uniqueness results will be proved via the theory of evolution operators; crucial tools in order to obtain such results will be a Nash inequality (proved for the first time in this general setting), and the proof of mapping properties of the evolution family associated to the problem.

These results are obtained in collaboration with M. R. Lancia (Sapienza Università di Roma).