Mean value properties of harmonic functions on Sierpinski gasket type fractals

TL;DR

This paper extends the classical mean value property of harmonic functions to the Sierpinski gasket and other symmetric fractals, providing new insights into their harmonic analysis.

Contribution

It establishes a mean value property for harmonic functions on Sierpinski gasket type fractals and extends it to other p.c.f. fractals with Dihedral-3 symmetry.

Findings

Mean value property holds for harmonic functions on Sierpinski gasket

Extension of the property to other p.c.f. fractals with Dihedral-3 symmetry

Provides a framework for harmonic analysis on 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.