Best constants for two families of higher order critical Sobolev embeddings

Itai Shafrir, Daniel Eli Spector*

*Corresponding author for this work

研究成果: Article同行評審

1 引文 斯高帕斯(Scopus)

摘要

In this paper we obtain the best constants in some higher order Sobolev inequalities in the critical exponent. These inequalities can be separated into two types: those that embed into [Formula presented] and those that embed into slightly larger target spaces. Concerning the former, we show that for [Formula presented], [Formula presented] even, one has an optimal constant [Formula presented] such that [Formula presented]for all [Formula presented] (the case [Formula presented] was handled in Shafrir, 2018). Meanwhile the most significant of the latter is a variation of D. Adams’ higher order inequality of J. Moser: For [Formula presented], [Formula presented] and [Formula presented], there exists [Formula presented] and optimal constant [Formula presented] such that [Formula presented]for all [Formula presented] such that [Formula presented], where [Formula presented] is the traditional semi-norm on the space [Formula presented].

原文English
頁(從 - 到)753-769
頁數17
期刊Nonlinear Analysis, Theory, Methods and Applications
177
DOIs
出版狀態Published - 1 十二月 2018

指紋 深入研究「Best constants for two families of higher order critical Sobolev embeddings」主題。共同形成了獨特的指紋。

引用此