Divergence Form Operators on Fractal-like Domains

✍ Scribed by Martin T. Barlow; Richard F. Bass

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 254 KB
• Volume: 175
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2000.3597

✦ Synopsis

We consider elliptic operators L in divergence form on certain domains in R d 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.