Revista Matemática Iberoamericana

Measure density and extendability of Sobolev functions

Piotr Hajłasz , Pekka Koskela , and Heli Tuominen

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Abstract

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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 24, Number 2 (2008), 645-669.

Dates
First available in Project Euclid: 11 August 2008

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1218475358

Mathematical Reviews number (MathSciNet)
MR2459208

Zentralblatt MATH identifier
1226.46029

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Keywords
Sobolev extension doubling measure

Citation

Hajłasz, Piotr; Koskela, Pekka; Tuominen, Heli. Measure density and extendability of Sobolev functions. Rev. Mat. Iberoamericana 24 (2008), no. 2, 645--669. https://projecteuclid.org/euclid.rmi/1218475358


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