On a two-phase problem for harmonic measure in general domains

Jonas Azzam; Mihalis Mourgoglou; Xavier Tolsa; Alexander Volberg

doi:10.1353/ajm.2019.0032

On a two-phase problem for harmonic measure in general domains

Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa, Alexander Volberg

Research output: Contribution to journal › Article › Research

2 Citations (Scopus)

Abstract

© 2019 by Johns Hopkins University Press. 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.

Original language	English
Pages (from-to)	1259-1279
Journal	American Journal of Mathematics
Volume	141
DOIs	https://doi.org/10.1353/ajm.2019.0032
Publication status	Published - 1 Oct 2019

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title = "On a two-phase problem for harmonic measure in general domains",

abstract = "{\textcopyright} 2019 by Johns Hopkins University Press. 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.",

author = "Jonas Azzam and Mihalis Mourgoglou and Xavier Tolsa and Alexander Volberg",

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AU - Mourgoglou, Mihalis

AU - Tolsa, Xavier

AU - Volberg, Alexander

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N2 - © 2019 by Johns Hopkins University Press. 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.

AB - © 2019 by Johns Hopkins University Press. 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.

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DO - 10.1353/ajm.2019.0032

M3 - Article

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EP - 1279

JO - American Journal of Mathematics

JF - American Journal of Mathematics

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