Open AccessBounds for subcritical best Sobolev constants in <i>W</i><sup>1, <i>p</i></sup>
Author(s) -
Lingling Du
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021135
Subject(s) - limiting , omega , combinatorics , sobolev space , mathematics , bounded function , physics , mathematical analysis , quantum mechanics , mechanical engineering , engineering
This paper aims at establishing fine bounds for subcritical best Sobolev constants of the embeddings\begin{document}$ W_{0}^{1,p}(\Omega)\hookrightarrow L^{q}(\Omega),\quad 1\leq q< \begin{cases} \frac{Np}{N-p},& 1\leq p<N\\ \infty,& p = N \end{cases} $\end{document}where \begin{document}$ N\geq p\geq1 $\end{document} and \begin{document}$ \Omega $\end{document} is a bounded smooth domain in \begin{document}$ \mathbb{R}^{N} $\end{document} or the whole space. The Sobolev limiting case \begin{document}$ p = N $\end{document} is also covered by means of a limiting procedure.