Best constants for two families of higher order critical Sobolev embeddings

Itai Shafrir, Daniel Eli Spector*

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

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].

Original languageEnglish
Pages (from-to)753-769
Number of pages17
JournalNonlinear Analysis, Theory, Methods and Applications
Volume177
DOIs
StatePublished - 1 Dec 2018

Keywords

  • Best constant
  • Critical exponent
  • Sobolev embedding

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