Approximation numbers of embeddings of Sobolev spaces (Q1910191)
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scientific article; zbMATH DE number 861943
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximation numbers of embeddings of Sobolev spaces |
scientific article; zbMATH DE number 861943 |
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Approximation numbers of embeddings of Sobolev spaces (English)
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31 March 1996
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Under appropriate hypotheses on the domain \(\Omega\) in \(\mathbb{R}^{2m}\), upper bounds for the approximation numbers of the compact embeddings of \(\mathring H^m(\Omega)\) in \(L_q(\Omega)\) \((q\geq 2)\) and in a suitable Orlicz space are obtained in terms of eigenvalues of \((- \Delta)^m\) with zero Dirichlet conditions. The case of Neumann boundary conditions is also discussed, as is the situation when these embeddings are not compact.
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approximation numbers
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compact embeddings
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Orlicz space
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eigenvalues
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Dirichlet conditions
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Neumann boundary conditions
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