Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus (Q2866502)
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scientific article; zbMATH DE number 6238321
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus |
scientific article; zbMATH DE number 6238321 |
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13 December 2013
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Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus (English)
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The authors investigate the existence and qualitative properties of extremals for inequalities NEWLINE\[NEWLINE|| u||^2_{C(\Omega)} \leq ||u||^2_{H^1(\Omega)}\left(C_1 \log \frac{||u||^2_{H^2(\Omega)}}{||u||^2_{H^1(\Omega)}} + C_2\right),NEWLINE\]NEWLINE where \(\Omega\) is a two-dimensional torus.
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