Coupling and Harnack inequalities for Sierpiński carpets
- 1 October 1993
- journal article
- Published by American Mathematical Society (AMS) in Bulletin of the American Mathematical Society
- Vol. 29 (2) , 208-212
- https://doi.org/10.1090/s0273-0979-1993-00424-5
Abstract
Uniform Harnack inequalities for harmonic functions on the pre-and graphical Sierpinski carpets are proved using a probabilistic coupling argument. Various results follow from this, including the construction of Brownian motion on Sierpinski carpets embedded in R d {\mathbb {R}^d} , d ≥ 3 d \geq 3 , estimates on the fundamental solution of the heat equation, and Sobolev and Poincaré inequalities.Keywords
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