The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (291 KB) | Metadata | Table of Contents | ZAA summary
Volume 21, Issue 1, 2002, pp. 113–133
DOI: 10.4171/ZAA/1067

Published online: 2002-03-31

A Transmission Problem with a Fractal Interface

Maria Rosaria Lancia[1]

(1) Università di Roma La Sapienza, Italy

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”.

Keywords: Fractal boundaries, Dirichlet forms, transmission problems

Lancia Maria Rosaria: A Transmission Problem with a Fractal Interface. Z. Anal. Anwend. 21 (2002), 113-133. doi: 10.4171/ZAA/1067