Guy David, Svitlana Mayboroda
Published 2020-07-03Version 1
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.
On $p$-Harmonic Measures in Half Spaces
Square Functions and the $A_\infty$ Property of Elliptic Measures
The Green function with pole at infinity applied to the study of the elliptic measure
![QR code for arXiv:2007.01745 [math.AP]](http://oss.arxitics.com/images/favicon.svg)