Revista Matemática Iberoamericana

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Volume 14, Issue 3, 1998, pp. 601–622
DOI: 10.4171/RMI/246

Published online: 1998-12-31

Hölder quasicontinuity of Sobolev functions on metric spaces

Piotr Hajlasz[1] and Juha Kinnunen[2]

(1) University of Warsaw, Poland
(2) Aalto University, Finland

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].

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Hajlasz Piotr, Kinnunen Juha: Hölder quasicontinuity of Sobolev functions on metric spaces. Rev. Mat. Iberoam. 14 (1998), 601-622. doi: 10.4171/RMI/246