Nonlocal Venttsel' diffusion in fractal-type domains: regularity results and numerical approximation

Abstract

We study a nonlocal Venttsel' problem in a non-convex bounded domain with a Koch-type boundary. Regularity results of the strict solution are proved in weighted Sobolev spaces. The numerical approximation of the problem is carried out and optimal a priori error estimates are obtained.

32 pages, 7 figures