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 (Ω, 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".
The energy form on a closed fractal curve F is constructed. As F is neither self-similar nor nested, it is regarded as a "fractal manifold". The energy is obtained by integrating the Lagrangian on F .
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