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# Nonlinear Theory and Its Applications, IEICEVol. 7 (2016) No. 3 pp. 386-394

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http://doi.org/10.1587/nolta.7.386

Special Section on Rigorous Nonlinear Analysis

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.