The singular strata of a free-boundary problem for harmonic measure
Sean McCurdy · Analysis & PDE · 2024
In this paper, we obtain \textit{quantitative} estimates on the fine structure of the singular set of the mutual boundary $\partial Ω^{\pm}$ for pairs of complementary domains, $Ω^+, Ω^- \subset \mathbb{R}^n$ 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, $\partial Ω^{\pm}.$