Estimation of Sobolev-type embedding constant on domains with minimally smooth boundary using extension operator

Kazuaki Tanaka*, Kouta Sekine, Makoto Mizuguchi, Shin’ichi Oishi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In this paper, we propose a method for estimating the Sobolev-type embedding constant from W 1,q(Ω)to Lp(Ω) on a domain Ω⊂Rn(n=2,3…) with minimally smooth boundary (also known as a Lipschitz domain), where p∈(n/(n−1),∞)q=np/(n+p). We estimate the embedding constant by constructing an extension operator from W1,q(Ω) to W1,q(Rn) and computing its operator norm. We also present some examples of estimating the embedding constant for certain domains.

Original languageEnglish
Article number389
Pages (from-to)1-23
Number of pages23
JournalJournal of Inequalities and Applications
Volume2015
Issue number1
DOIs
Publication statusPublished - 2015 Dec 1

Keywords

  • Sobolev inequality
  • embedding constant
  • extension operator

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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