Transformations that preserve Sobolev spaces (Q1073210)
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scientific article; zbMATH DE number 3944222
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Transformations that preserve Sobolev spaces |
scientific article; zbMATH DE number 3944222 |
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Transformations that preserve Sobolev spaces (English)
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1984
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The following theorem is proved: If the mapping \(\phi\) : \(G\to G'\) between the domains G and G' in \({\mathbb{R}}^ n\) induces an isomorphism \(\phi^*: W^ 1_ p(G')\to W^ 1_ p(G)\) between the Sobolev-spaces with index p where \(p\in (n-1,n)\) then \(\phi\) coincides a.e. with a quasi-isometry.
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quasi-isometry
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