TY - JOUR
T1 - Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains
AU - Mizuguchi, Makoto
AU - Tanaka, Kazuaki
AU - Sekine, Kouta
AU - Oishi, Shin’ichi
N1 - Funding Information:
This work was supported by CREST, Japan Science and Technology Agency. The second author (KT) was supported by JSPS Grant-in-Aid for Research Activity Start-up Grant Number JP17H07188 and Mizuho Foundation for the Promotion of Sciences. The third author (KS) was supported by JSPS KAKENHI Grant Number 16K17651. We thank the editors and reviewers for giving useful comments to improve the contents of this manuscript.
Publisher Copyright:
© 2017, The Author(s).
PY - 2017
Y1 - 2017
N2 - This paper is concerned with an explicit value of the embedding constant from W1 , q(Ω) to Lp(Ω) for a domain Ω ⊂ RN (N∈ N), where 1 ≤ q≤ p≤ ∞. We previously proposed a formula for estimating the embedding constant on bounded and unbounded Lipschitz domains by estimating the norm of Stein’s extension operator. Although this formula can be applied to a domain Ω that can be divided into a finite number of Lipschitz domains, there was room for improvement in terms of accuracy. In this paper, we report that the accuracy of the embedding constant is significantly improved by restricting Ω to a domain dividable into bounded convex domains.
AB - This paper is concerned with an explicit value of the embedding constant from W1 , q(Ω) to Lp(Ω) for a domain Ω ⊂ RN (N∈ N), where 1 ≤ q≤ p≤ ∞. We previously proposed a formula for estimating the embedding constant on bounded and unbounded Lipschitz domains by estimating the norm of Stein’s extension operator. Although this formula can be applied to a domain Ω that can be divided into a finite number of Lipschitz domains, there was room for improvement in terms of accuracy. In this paper, we report that the accuracy of the embedding constant is significantly improved by restricting Ω to a domain dividable into bounded convex domains.
KW - Hardy-Littlewood-Sobolev inequality
KW - Sobolev embedding constant
KW - Young inequality
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U2 - 10.1186/s13660-017-1571-0
DO - 10.1186/s13660-017-1571-0
M3 - Article
AN - SCOPUS:85037051995
SN - 1025-5834
VL - 2017
JO - Journal of Inequalities and Applications
JF - Journal of Inequalities and Applications
M1 - 299
ER -