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arXiv · 1904.09361

The Singular Strata of a Free-Boundary problem for harmonic measure

Sean McCurdy
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Abstract

In this paper, we obtain \textit{quantitative} estimates on the fine structure of the singular set of the mutual boundary $\partial \Omega^{\pm}$ for pairs of complementary domains, $\Omega^+, \Omega^- \subset \mathbb{R}^n$ 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, $\partial \Omega^{\pm}.$

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Sean McCurdy. 2019-04-19. The Singular Strata of a Free-Boundary problem for harmonic measure. https://doi.org/10.2140/apde.2024.17.1127

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