An example of a functional which is weakly lower semicontinuous on \(W_0^{1,p}\) for every \(p>2\) but not on \(H_0^1\) (Q628815)
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scientific article; zbMATH DE number 5862056
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An example of a functional which is weakly lower semicontinuous on \(W_0^{1,p}\) for every \(p>2\) but not on \(H_0^1\) |
scientific article; zbMATH DE number 5862056 |
Statements
An example of a functional which is weakly lower semicontinuous on \(W_0^{1,p}\) for every \(p>2\) but not on \(H_0^1\) (English)
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7 March 2011
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Summary: We give an example of a functional which is defined and coercive on \(H^1_0(\Omega)\), which is sequentially weakly lower semicontinuous on \(W^{1,p}_0(\Omega)\) for every \(p>2\), but which is not sequentially lower semicontinuous on \(H^{1}_0(\Omega)\). This functional is non local.
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lower semicontinuity
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Hardy-Sobolev inequalities
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