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RESEARCH PRODUCT

Sobolev embeddings, extensions and measure density condition

Pekka KoskelaHeli TuominenPiotr Hajłasz

subject

Discrete mathematicsExtension operator010102 general mathematicsEberlein–Šmulian theoremMeasure density condition01 natural sciencesSobolev embeddingSobolev inequality010101 applied mathematicsSobolev spaceCorollarySobolev spaces0101 mathematicsInvariant (mathematics)AnalysisEdge-of-the-wedge theoremSobolev spaces for planar domainsMathematicsTrace operator

description

AbstractThere 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.

yearjournalcountryeditionlanguage
2008-03-01Journal of Functional Analysis
https://doi.org/10.1016/j.jfa.2007.11.020