Hölder quasicontinuity of Sobolev functions on metric spaces (Q1283344)
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scientific article; zbMATH DE number 1275454
| Language | Label | Description | Also known as |
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| English | Hölder quasicontinuity of Sobolev functions on metric spaces |
scientific article; zbMATH DE number 1275454 |
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Hölder quasicontinuity of Sobolev functions on metric spaces (English)
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13 April 1999
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Summary: 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 \textit{J. Malý} [Potential Anal. 2, No. 3, 249--254 (1993; Zbl 0803.46037)] to the Sobolev spaces on metric spaces [\textit{P. Hajłasz}, Potential Anal. 5, No. 4, 403--415 (1996; Zbl 0859.46022)].
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