Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
Special Section on Rigorous Nonlinear Analysis
On the embedding constant of the Sobolev type inequality for fractional derivatives
Makoto MizuguchiAkitoshi TakayasuTakayuki KuboShin'ichi Oishi
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Volume 7 (2016) Issue 3 Pages 386-394

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This paper is concerned with the embedding constant of the Sobolev type inequality for fractional derivatives on $\Omega\subset\mathbb{R}^{N}~(N\in\mathbb{N})$. The constant is explicitly described using the analytic semigroup over L2(Ω) generated by the Laplace operator. Some numerical examples of estimating the embedding constant are also provided.