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 R-3 in the case of a Koch-type fractal layer S or the corresponding prefractal layer approximating S. 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. (C) 2012 Elsevier Ltd. All rights reserved