A counterexample regarding a two-phase problem for harmonic measure in VMO
A counterexample regarding a two-phase problem for harmonic measure in VMO
Abstract Let $\Omega^+\subset\mathbb R^{n+1}$ be a vanishing Reifenberg flat domain such that $\Omega^+$ and $\Omega^-=\mathbb R^{n+1}\setminus\overline {\Omega^+}$ have joint big pieces of chord-arc subdomains and such that the outer unit normal to $\partial\Omega^+$ belongs to $VMO(\omega^+)$, where $\omega^\pm$ is the harmonic measure in $\Omega^\pm$. Up to now it was an …