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The singular strata of a free-boundary problem for harmonic measure

Sean McCurdy

Vol. 17 (2024), No. 4, 1127–1173
Abstract

We obtain quantitative estimates on the fine structure of the singular set of the mutual boundary Ω± for pairs of complementary domains Ω+,Ω n which arise in a class of two-sided free boundary problems for harmonic measure. These estimates give new insight into the structure of the mutual boundary Ω±.

Keywords
free-boundary, harmonic measure, partial regularity, singular strata
Mathematical Subject Classification 2010
Primary: 31B05, 31B25, 35R35
Milestones
Received: 24 April 2019
Revised: 19 November 2021
Accepted: 23 September 2022
Published: 17 May 2024
Authors
Sean McCurdy
National Taiwan Normal University
Taipei City
Taiwan

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