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The Singular Strata of a Free-Boundary problem for harmonic measure (1904.09361v2)
Published 19 Apr 2019 in math.AP
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, $\partial \Omega{\pm}.$