Sobolev embeddings , extensions and measure density condition

  title={Sobolev embeddings , extensions and measure density condition},
  author={Piotr Hajłasz and Pekka Koskela and Heli Tuominen},
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 Wm,p-extension domains for 1 < p < ∞. As a corollary we prove that the property of being a W1,p-extension domain, 1 < p ∞, is invariant under bi-Lipschitz mappings, Theorem 8. © 2007 Elsevier Inc. All rights… CONTINUE READING

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