A Transmission Problem with a Fractal Interface

  • Maria Rosaria Lancia

    Università di Roma La Sapienza, Italy


In this paper we study a transmission problem with a fractal interface KK, where a second order transmission condition is imposed. We consider the case in which the interface KK is the Koch curve and we prove existence and uniqueness of the weak solution of the problem in V(Ω,K)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”.

Cite this article

Maria Rosaria Lancia, A Transmission Problem with a Fractal Interface. Z. Anal. Anwend. 21 (2002), no. 1, pp. 113–133

DOI 10.4171/ZAA/1067