Good elliptic operators on Cantor sets

Guy David; Svitlana Mayboroda

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arXiv · 2007.01745

Good elliptic operators on Cantor sets

Guy David·Svitlana Mayboroda

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Abstract

It is well known that a purely unrectifiable set cannot support a harmonic measure which is absolutely continuous with respect to the Hausdorff measure of this set. We show that nonetheless there exist elliptic operators on (purely unrectifiable) Cantor sets in ${\mathbb{R}}^2$ whose elliptic measure is absolutely continuous, and in fact, essentially proportional to the Hausdorff measure.

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Guy David, Svitlana Mayboroda. 2020-07-03. Good elliptic operators on Cantor sets. https://arxiv.org/abs/2007.01745

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