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Hajłasz, Piotr; Koskela, Pekka; Tuominen, Heli

Measure density and extendability of Sobolev functions. (English) Zbl 1226.46029

Rev. Mat. Iberoam. 24, No. 2, 645-669 (2008).
Summary: 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.

Cited in 1 Review
Cited in 35 Documents

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
30L99 Analysis on metric spaces

Keywords:

Sobolev extension; doubling measure
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\textit{P. Hajłasz} et al., Rev. Mat. Iberoam. 24, No. 2, 645--669 (2008; Zbl 1226.46029)
Full Text: DOI Euclid

References:

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