Interpolation inequalities for derivatives in variable exponent Lebesgue–Sobolev spaces
By Aibin Zang, Yong Fu. 2008
141 citations recorded by the source corpus.
Abstract We show the interpolation inequalities for derivatives in variable exponent Lebesgue–Sobolev spaces by applying the boundedness of the Hardy–Littlewood maximal operator on L p ( ⋅ ) . As applications, we prove a new Landau–Komogorov type inequality for the second-order derivative and an embedding theorem and discuss the equivalent norms in the space W 0 1 , p ( ⋅ ) ( Ω ) ∩ W 2 , p ( ⋅ ) ( Ω ) .
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/73d6aa7ba089680403bf23ad37efdb6ab3b648c8
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In Applied Mathematics
- Khaled Kefi
- Vicentiu D. Rădulescu
- Dušan D. Repovš
- Zhijun Zhang
- Anouar Bahrouni
- Marius Ghergu
- V. Ruadulescu
- K. Kefi
Citations in the corpus
- On a p(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{p(x)}$$\end{document}-biharmonic problem with singula (2017, background): “In Zang and Fu [28], the equivalence of the norms was proved, and it was even proved that the norm |Δu|p(x) is equivalent to the norm ‖u‖ (see [28, Theorem 4.”