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

Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains This paper is concerned with an explicit value of the embedding constant from W 1 , q ( Ω ) $W^{1,q}(\Omega)$ to L p ( Ω ) $L^{p}(\Omega)$ for a domain Ω ⊂ R N $\Omega\subset\mathbb{R}^{N}$ ( N ∈ N $N\in\mathbb{N}$ ), where 1 ≤ q ≤ p ≤ ∞ $1\leq q\leq p\leq\infty$ . 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inequalities and Applications Springer Journals

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

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by The Author(s)
Subject
Mathematics; Analysis; Applications of Mathematics; Mathematics, general
eISSN
1029-242X
D.O.I.
10.1186/s13660-017-1571-0
Publisher site
See Article on Publisher Site

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