# Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains

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

*この研究の対応する著者

18 被引用数 (Scopus)

## 抄録

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.

本文言語 English 299 Journal of Inequalities and Applications 2017 https://doi.org/10.1186/s13660-017-1571-0 Published - 2017

• 分析
• 離散数学と組合せ数学
• 応用数学

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