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Coupling and Harnack inequalities for Sierpinski carpets

Martin T. Barlow·Richard F. Bass
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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 $\R^d$, $d\geq 3$, estimates on the fundamental solution of the heat equation, and Sobolev and Poincar\'e inequalities.

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Martin T. Barlow, Richard F. Bass. 1993-10-01. Coupling and Harnack inequalities for Sierpinski carpets. https://arxiv.org/abs/math/9310225

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