$\epsilon$-Approximability of Harmonic Functions in $L^p$ Implies Uniform Rectifiability

Simon Bortz, Olli Tapiola

Suppose that $\Omega \subset {\mathbb{R}}^{n+1}$, $n\ge 2$, is an open set satisfying the corkscrew condition with an $n$-dimensional ADR boundary, $\partial \Omega$. In this note, we show tha…