Special Session 39: Recent results in local and nonlocal elliptic and parabolic equations

Non autonomous BVPs in extension domains with dynamical boundary conditions

maria rosaria lancia
Sapienza
Italy
Co-Author(s):    
Abstract:
I will consider a parabolic semi-linear non autonomous problem, both for local and nonlocal operators, with dynamical boundary conditions, in an extension domain with boundary a d-set. Such problems are also known in the literature as Venttsel problems. Existence and uniqueness of the mild solution of the associated semi-linear abstract Cauchy problem are proved as well as regularity results. This is a part of a long term project with S.Creo and P.Vernole.