Revista Matemática Iberoamericana
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Measure density and extendability of Sobolev functionsPiotr Hajłasz, Pekka Koskela and Heli Tuominen (1) Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, PA 15260, PITTSBURGH, UNITED STATES
(2) Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, 40014, JYVÄSKYLÄ, FINLAND
(3) Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FIN-40351, JYVÄSKYLÄ, FINLAND
We study necessary and sufficient conditions for a domain to be a Sobolev extension domain in the setting of metric measure spaces. In particular, we prove that extension domains must satisfy a measure density condition.
Keywords: Sobolev extension, doubling measure
Hajłasz P, Koskela P, Tuominen H. Measure density and extendability of Sobolev functions. Rev. Mat. Iberoamericana 24 (2008), 645-669. doi: 10.4171/RMI/551