Nonlocal Venttsel-type problems in irregular domains: well posedness, regularity results and their approximation

We consider nonlocal Venttsel problems, possibly non autonomous, in irregular domains with fractal-type boundaries. We prove well posedness and regularity results. In view of numerical approximations, we study the corresponding problems $P_n$ in suitable approximating piecewise smooth domains $\Omega_n,$ We prove that the solution of the fractal problem is indeed the limit of the sequence of the so-called prefractal solutions.