Sharp numerical inclusion of the best constant for embedding H0 1(Ω)↪Lp(Ω) on bounded convex domain

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3 Citations (Scopus)

Abstract

In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding H0 1(Ω)↪Lp(Ω) on a bounded convex domain in R2. We estimate the best constant by computing the corresponding extremal function using a verified numerical computation. Verified numerical inclusions of the best constant on a square domain are presented.

Original languageEnglish
Pages (from-to)306-313
Number of pages8
JournalJournal of Computational and Applied Mathematics
Volume311
DOIs
Publication statusPublished - 2017 Feb 1

Fingerprint

Best Constants
Convex Domain
Bounded Domain
Inclusion
Extremal Function
Numerical methods
Numerical Computation
Numerical Methods
Computing
Estimate

Keywords

  • Computer-assisted proof
  • Elliptic problem
  • Embedding constant
  • Error bounds
  • Sobolev inequality
  • Verified numerical computation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

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abstract = "In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding H0 1(Ω)↪Lp(Ω) on a bounded convex domain in R2. We estimate the best constant by computing the corresponding extremal function using a verified numerical computation. Verified numerical inclusions of the best constant on a square domain are presented.",
keywords = "Computer-assisted proof, Elliptic problem, Embedding constant, Error bounds, Sobolev inequality, Verified numerical computation",
author = "Kazuaki Tanaka and Kouta Sekine and Makoto Mizuguchi and Shinichi Oishi",
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AU - Tanaka, Kazuaki

AU - Sekine, Kouta

AU - Mizuguchi, Makoto

AU - Oishi, Shinichi

PY - 2017/2/1

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AB - In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding H0 1(Ω)↪Lp(Ω) on a bounded convex domain in R2. We estimate the best constant by computing the corresponding extremal function using a verified numerical computation. Verified numerical inclusions of the best constant on a square domain are presented.

KW - Computer-assisted proof

KW - Elliptic problem

KW - Embedding constant

KW - Error bounds

KW - Sobolev inequality

KW - Verified numerical computation

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JO - Journal of Computational and Applied Mathematics

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