In this paper we study a transmission problem with a fractal interface K , where a second order transmission condition is imposed. We consider the case in which the interface K is the Koch curve and we prove existence and uniqueness of the weak solution of the problem in V (\Omega, K) , a suitable ”energy space”. The link between the variational formulation and the problem is possible once we recover a version of the Gauss-Green formula for fractal boundaries, hence a definition of ”normal derivative”.

We study a nonsteady transmission problem across either a fractal layer S or the corresponding prefractal layer $S_h$. The transmission condition is of order two. Existence, uniqueness, and regularity results for the strict solution, in both cases, are established as well as convergence results for the solutions of the approximating problems in varying Hilbert spaces.