Harmonic measure and quantitative connectivity: geometric characterization of the $L^p$ solvability of the Dirichlet problem. Part II

Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa

Let $\Omega \subset {\mathbb{R}}^{n+1}$ be an open set with $n$-AD-regular boundary. In this paper we prove that if the harmonic measure for $\Omega$ satisfies the so-called weak-$A_{\infty }$ condi…