Revista Matemática Iberoamericana

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

Published online: 2008-08-31

Measure density and extendability of Sobolev functions

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

(1) University of Pittsburgh, USA
(2) University of Jyväskylä, Finland
(3) University of 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 Piotr, Koskela Pekka, Tuominen Heli: Measure density and extendability of Sobolev functions. Rev. Mat. Iberoam. 24 (2008), 645-669. doi: 10.4171/RMI/551