Sobolev embeddings, extensions and measure density condition

Abstract: There are two main results in the paper. In the first one, Theorem 1, we prove that if the Sobolev embedding theorem holds in Ω, in any of all the possible cases, then Ω satisfies the measure density condition. The second main result, Theorem 5, provides several characterizations of the -extension domains for . As a corollary we prove that the property of being a -extension domain, , is invariant under bi-Lipschitz mappings, Theorem 8. [Copyright &y& Elsevier]