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Zeitschrift für Analysis und ihre Anwendungen


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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