Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2002-03-31
A Transmission Problem with a Fractal InterfaceMaria Rosaria Lancia (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