Semilinear fractal problems: Approximation and regularity results

We prove existence and uniqueness of the weak solution for a second order semilinear transmission problem in a bounded domain in R3R3 in the case of a Koch-type fractal layer SS or the corresponding prefractal layer approximating SS. We study the asymptotic behavior of the solutions of the corresponding prefractal problem and we prove regularity results for the weak solution via a generalized Green formula for domains with fractal boundaries.