A geometric characterization of planar Sobolev extension domains

Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang

We characterize bounded simply-connected planar $W^{1,p}$-extension domains for $1<p<2$ as those bounded domains $\Omega \subset {\mathbb{R}}^2$ for which any two points $z_1,z_2 \in \ma…