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

Research output: Contribution to journalArticle

1 Citation (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

Fingerprint

Extension Operator
Lipschitz Domains
Operator Norm
Computing
Estimate

Keywords

  • embedding constant
  • extension operator
  • Sobolev inequality

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

@article{82aa1519f1e04d0395b99f3dccf6e93b,
title = "Estimation of Sobolev-type embedding constant on domains with minimally smooth boundary using extension operator",
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.",
keywords = "embedding constant, extension operator, Sobolev inequality",
author = "Kazuaki Tanaka and Kouta Sekine and Makoto Mizuguchi and Shinichi Oishi",
year = "2015",
month = "12",
day = "1",
doi = "10.1186/s13660-015-0907-x",
language = "English",
volume = "2015",
pages = "1--23",
journal = "Journal of Inequalities and Applications",
issn = "1025-5834",
publisher = "Springer Publishing Company",
number = "1",

}

TY - JOUR

T1 - Estimation of Sobolev-type embedding constant on domains with minimally smooth boundary using extension operator

AU - Tanaka, Kazuaki

AU - Sekine, Kouta

AU - Mizuguchi, Makoto

AU - Oishi, Shinichi

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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.

KW - embedding constant

KW - extension operator

KW - Sobolev inequality

UR - http://www.scopus.com/inward/record.url?scp=84949548203&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949548203&partnerID=8YFLogxK

U2 - 10.1186/s13660-015-0907-x

DO - 10.1186/s13660-015-0907-x

M3 - Article

VL - 2015

SP - 1

EP - 23

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

SN - 1025-5834

IS - 1

M1 - 389

ER -