JournalsrmiVol. 14, No. 3pp. 601–622

Hölder quasicontinuity of Sobolev functions on metric spaces

  • Piotr Hajłasz

    University of Warsaw, Poland
  • Juha Kinnunen

    Aalto University, Finland
Hölder quasicontinuity of Sobolev functions on metric spaces cover
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Abstract

We prove that every Sobolev function defined on a metric space coincides with a Hölder continuous function outside a set of small Hausdorff content or capacity. Moreover, the Hölder continuous function can be chosen so that it approximates the given function in the Sobolev norm. This is a generalization of a result of Maly [Ma1] to the Sobolev spaces on metric spaces [H1].

Cite this article

Piotr Hajłasz, Juha Kinnunen, Hölder quasicontinuity of Sobolev functions on metric spaces. Rev. Mat. Iberoam. 14 (1998), no. 3, pp. 601–622

DOI 10.4171/RMI/246