Sharp numerical inclusion of the best constant for embedding H01(Ω)↪Lp(Ω) on bounded convex domain

Kazuaki Tanaka; Kouta Sekine; Makoto Mizuguchi; Shin'ichi Oishi

doi:10.1016/j.cam.2016.07.021

Sharp numerical inclusion of the best constant for embedding H₀¹(Ω)↪L^p(Ω) on bounded convex domain

Kazuaki Tanaka^*, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding H₀¹(Ω)↪L^p(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 language	English
Pages (from-to)	306-313
Number of pages	8
Journal	Journal of Computational and Applied Mathematics
Volume	311
DOIs	https://doi.org/10.1016/j.cam.2016.07.021
Publication status	Published - 2017 Feb 1

Keywords

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

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.cam.2016.07.021

Cite this

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title = "Sharp numerical inclusion of the best constant for embedding H01(Ω)↪Lp(Ω) on bounded convex domain",

abstract = "In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding H01(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 Shin'ichi Oishi",

note = "Funding Information: Technical Research Council (CONICET) under Grant PIP 2013-2015 GI, 11220120100202CO; and Fundaci{\'o}n Articular, Quilmes, Argentina. Funding Information: Funding: this work was supported by the Argentinean National Scientific and Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

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AU - Tanaka, Kazuaki

AU - Sekine, Kouta

AU - Mizuguchi, Makoto

AU - Oishi, Shin'ichi

N1 - Funding Information: Technical Research Council (CONICET) under Grant PIP 2013-2015 GI, 11220120100202CO; and Fundación Articular, Quilmes, Argentina. Funding Information: Funding: this work was supported by the Argentinean National Scientific and Publisher Copyright: © 2016 Elsevier B.V.

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Y1 - 2017/2/1

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KW - Computer-assisted proof

KW - Elliptic problem

KW - Embedding constant

KW - Error bounds

KW - Sobolev inequality

KW - Verified numerical computation

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