Abstract
We prove that every Sobolev function defined on a metric space coincides with a Holder 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 Malý [Ma1] to the Sobolev spaces on metric spaces [H1].
| Original language | English |
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| Pages (from-to) | 601-622 |
| Number of pages | 22 |
| Journal | Revista Matematica Iberoamericana |
| Volume | 14 |
| Issue number | 3 |
| Publication status | Published - 1998 |
| MoE publication type | A1 Journal article-refereed |