Potential theory on the Sierpinski gasket (Q915269)

The Sierpinski gasket X is a compact, finitely ramified, self-similar fractal embedded in \({\mathbb{R}}^ n\), \(n\geq 2\), of Hausdorff dimension \(\ln (n+1)/\ln 2.\) The author develops in a short and elementary way a potential theory of harmonic kernels on X. It is shown: The harmonic functions form a \({\mathcal P}\)-harmonic space which gives the existence of a ``Brownian motion'' on X. There exists a finite, symmetric Green function, which is the kernel of the inverse operator of the associated infinitesimal generator. Harmonic functions are a.s. differentiable with derivative 0 with respect to the appropriate Hausdorff measure.