JournalsrmiVol. 24, No. 2pp. 645–669

Measure density and extendability of Sobolev functions

  • Piotr Hajłasz

    University of Pittsburgh, USA

  • Pekka Koskela

    University of Jyväskylä, Finland

  • Heli Tuominen

    University of Jyväskylä, Finland
Measure density and extendability of Sobolev functions cover
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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.

Cite this article

Piotr Hajłasz, Pekka Koskela, Heli Tuominen, Measure density and extendability of Sobolev functions. Rev. Mat. Iberoam. 24 (2008), no. 2, pp. 645–669

DOI 10.4171/RMI/551