Maximally singular Sobolev functions (Q1772373)
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scientific article; zbMATH DE number 2157698
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maximally singular Sobolev functions |
scientific article; zbMATH DE number 2157698 |
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Maximally singular Sobolev functions (English)
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18 April 2005
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In any Sobolev space \(W^{m,p}(\mathbb{R}^N)\) with \(p>1\), \(mp\leq N\), a function is constructed, the set of singular points of which has the maximal possible Hausdorff dimension equal to \(N-mp\). The analogous result is proven also for Bessel potential spaces \(L^{\alpha,p}(\mathbb{R})\) with \(\alpha>0\), \(p>1\).
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Sobolev spaces
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Bessel potential space
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Hausdorff dimension
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singular point
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