A Transmission Problem with a Fractal Interface | Zendy

Maria Rosaria Lancia | Zendy

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A Transmission Problem with a Fractal Interface

Author(s) -

Maria Rosaria Lancia

Publication year - 2002

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1067

Subject(s) - fractal , interface (matter) , transmission (telecommunications) , computer science , topology (electrical circuits) , mathematics , mathematical analysis , telecommunications , parallel computing , combinatorics , bubble , maximum bubble pressure method

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”.

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