Sobolev gradients in uniformly convex spaces (Q1024985)
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scientific article; zbMATH DE number 5566215
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sobolev gradients in uniformly convex spaces |
scientific article; zbMATH DE number 5566215 |
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Sobolev gradients in uniformly convex spaces (English)
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18 June 2009
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Let \(H^{1,p}[0,1]\) be the Sobolev space with the norm \[ \| f\|= \Biggl(\int^1_0 |f|^p+ |f'|^p\Biggr)^{{1\over p}},\;f\in H^{1,p}[0,1],\;p> 2. \] One of the main results of this article is the proof that the dual s pace \((H^{1,q}[0,1])^*\) of the space \(H^{1,q}[0,1]\), \(q> 2\), is isomorphic to the space \(H^{1,p}[0,1]\), where \({1\over q}+{1\over p}= 1\).
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