Revista Matemática Iberoamericana


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Volume 24, Issue 2, 2008, pp. 645–669
DOI: 10.4171/RMI/551

Measure density and extendability of Sobolev functions

Piotr Hajłasz[1], Pekka Koskela[2] and Heli Tuominen[3]

(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