On a two-phase problem for harmonic measure in general domains
Classical Analysis and ODEs
2016-09-21 v1 Analysis of PDEs
Abstract
We show that, for disjoint domains in the Euclidean space, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries. This improves on our previous result which assumed that the boundaries satisfied the capacity density condition.
Cite
@article{arxiv.1609.06133,
title = {On a two-phase problem for harmonic measure in general domains},
author = {Jonas Azzam and Mihalis Mourgoglou and Xavier Tolsa and Alexander Volberg},
journal= {arXiv preprint arXiv:1609.06133},
year = {2016}
}