Uniform and Sobolev extension domains

We prove that if a domain DcR" is quasiconformally equivalent to a uniform domain, then D is an extension domain for the Sobolev class W/¡ if and only if D is locally uniform. We provide examples which suggest that this result is best possible. We exhibit a list of equivalent conditions for domains quasiconformally equivalent to uniform domains, one of which characterizes the quasiconformal homeomorphisms between uniform and locally uniform domains.