On the embedding constant of the Sobolev type inequality for fractional derivatives

Abstract

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.