Uniform rectifiability and $\epsilon$-approximability of harmonic functions in $L^p$

Steve Hofmann, Olli Tapiola

Suppose that $E\subset {\mathbb{R}}^{n+1}$ is a uniformly rectifiable set of codimension $1$. We show that every harmonic function is $\epsilon$-approximable in $L^p(\Omega )$ for ever…