Mean value properties of harmonic functions on Sierpinski gasket type fractals

Abstract

In this paper, we establish an analogue of the classical mean value property for both the harmonic functions and some general functions in the domain of the Laplacian on the Sierpinski gasket. Furthermore, we extend the result to some other p.c.f. fractals with Dihedral-3 symmetry.

arXiv comment27 pages, 9 figures, to appear, JFAA