On the Brezis and Mironescu conjecture concerning a Gagliardo--Nirenberg inequality for fractional Sobolev norms. (Q1406915)
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scientific article; zbMATH DE number 1975956
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Brezis and Mironescu conjecture concerning a Gagliardo--Nirenberg inequality for fractional Sobolev norms. |
scientific article; zbMATH DE number 1975956 |
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On the Brezis and Mironescu conjecture concerning a Gagliardo--Nirenberg inequality for fractional Sobolev norms. (English)
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7 September 2003
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It is the main aim of this paper to prove the inequality \[ \| u \, | W^{\theta s}_{p/ \theta} (\mathbb{R}^n) \| \leq c(p, s, \theta) \, \| u \, | W^s_p (\mathbb{R}^n) \| ^\theta \, \| u \, | L_\infty (\mathbb{R}^n) \| ^{1- \theta}, \] where \(0<s<1\), \( 1<p< \infty\), \(0 < \theta <1\), and to estimate the constant \(c(p,s, \theta)\) in an optimal way.
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Gagliardo-Nirenberg inequality
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