On the minimality of the \(p\)-harmonic map \(\frac{x}{|x|}:B^n\to S^{n-1}\) (Q5956937)
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scientific article; zbMATH DE number 1713842
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the minimality of the \(p\)-harmonic map \(\frac{x}{|x|}:B^n\to S^{n-1}\) |
scientific article; zbMATH DE number 1713842 |
Statements
On the minimality of the \(p\)-harmonic map \(\frac{x}{|x|}:B^n\to S^{n-1}\) (English)
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31 July 2002
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The author proves that for any real number \(1<p\leq n-1\), the map \({x\over |x|}:B^n\rightarrow S^{n-1}\) is the unique minimizer of the \(p\)-energy functional \(\int_{B^n}|\nabla u|^p dx\) among all maps in \(W^{1,p}(B^n,S^{n-1})\) with boundary value \(x\) on \(\partial B^n\).
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\(p\)-energy
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\(p\)-harmonic map
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minimality
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