The best constant for an almost critical Sobolev imbedding (Q1049758)
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scientific article; zbMATH DE number 5657893
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The best constant for an almost critical Sobolev imbedding |
scientific article; zbMATH DE number 5657893 |
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The best constant for an almost critical Sobolev imbedding (English)
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13 January 2010
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Summary: The inequality \[ \|u\|_\infty\leq\frac{C}{\sqrt{\varepsilon}}\,\|u\|_{H^{N/2+\varepsilon}}\text{ for all }u\in H^{N/2+\varepsilon}(\Omega), \] is shown for \(\Omega\) a sufficiently smooth domain in \(\mathbb R^N\) or a product of \(N\) bounded open intervals. This inequality is optimal for any open domain \(\Omega\).
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best constant
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Sobolev imbedding
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