We consider second order transmission problems across Koch-type curves formulated as boundary value problems for elliptic operators in a quasi-filling geometry for the fibers. We use a variational approach and the M-convergence methods. We prove that the solution of the transmission problem across a Koch-type curve is the limit of the solutions of suitable second order transmission problems across polygonal curves.
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Raffaela Capitanelli, Maria Agostina Vivaldi, Quasi-filling fractal layers. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 4, pp. 465–473DOI 10.4171/RLM/716