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Boundary Value Problems for a Family of Domains in the Sierpinski Gasket

For a family of domains in the Sierpinski gasket, we study harmonic functions of finite energy, characterizing them in terms of their boundary values, and study their normal derivatives on the boundary. We characterize those domains for which there is an extension operator for functions of finite energy. We give an explicit construction of the Green's function for these domains.

preprint2013arXivOpen access
Zijian GuoHua QiuRobert S. Strichartz
math.FAmath.CA
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Zijian GuoHua QiuRobert S. Strichartz

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