Abstract
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We obtain
quantitative estimates on the fine structure of the singular set of the mutual boundary
for pairs of
complementary domains
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
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Keywords
free-boundary, harmonic measure, partial regularity,
singular strata
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Mathematical Subject Classification 2010
Primary: 31B05, 31B25, 35R35
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Milestones
Received: 24 April 2019
Revised: 19 November 2021
Accepted: 23 September 2022
Published: 17 May 2024
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Publishers). Distributed under the Creative Commons
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