The two-phase problem for harmonic measure in VMO

Martí Prats, Xavier Tolsa

Let ${\Omega }^{+}\subset {\mathbb{R}}^{n+1}$ be an NTA domain and let ${\Omega }^{-}={\mathbb{R}}^{n+1}\setminus \overline{{\Omega }^{+}}$ be an NTA domain as well. Denote by ${\omega }^{+}$ and ${\omega }^{-}$ their respective harmoni…