A Transmission Problem with a Fractal Interface
Maria Rosaria Lancia · Zeitschrift für Analysis und ihre Anwendungen · 2002
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”.