Divergence Form Operators on Fractal-like Domains

Abstract

We consider elliptic operators L in divergence form on certain domains in Rd with fractal volume growth. The domains we look at are pre-Sierpinski carpets, which are derived from higher dimensional Sierpinski carpets. We prove a Harnack inequality for non-negative L-harmonic functions on these domains and establish upper and lower bounds for the corresponding heat equation. © 2000 Academic Press.