A formula for the functions realizing functionals (Q2773638)
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scientific article; zbMATH DE number 1710263
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A formula for the functions realizing functionals |
scientific article; zbMATH DE number 1710263 |
Statements
24 February 2002
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fundamental solution
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convolution
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Sobolev spaces
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polyharmonic equation
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A formula for the functions realizing functionals (English)
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Using results of his previous article [Sib. Math. J. 38, No. 1, 140--146 (1997; Zbl 0868.46022)], the author proves the formula NEWLINE\[NEWLINE u(x)=(-1)^m\lim_{\varepsilon\to 0}\int\limits_{E_n} \sum\limits_{|\alpha|=m}K_\alpha (x,y)(l\circ G_{\varepsilon}^{(\alpha)})(y) dy NEWLINE\]NEWLINE for the functions \(u\) realizing functionals \(l\) in Sobolev spaces.
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