Vernescu, Bogdan M.
In this paper we study the standard Dirichlet form and its associated energy measures and Laplacians on the Sierpinski gasket, and Related fractals constructed by Kigami. We first obtain a pointwise formula for the Kusuoka Laplacian, and then the intersection of its domain and that of the standard Laplacian is shown to be the set of harmonic functions. The standard measure is then shown to be the only one with respect to which the harmonic functions satisfy a certain type of mean value property.
Worcester Polytechnic Institute
Major Qualifying Project
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