Uniform and Sobolev Extension Domains
Uniform and Sobolev Extension Domains
We prove that if a domain $D \subset {{\mathbf {R}}^n}$ is quasiconformally equivalent to a uniform domain, then $D$ is an extension domain for the Sobolev class $W_n^1$ if and only if $D$ is locally uniform. We provide examples which suggest that this result is best possible. We exhibit a …