Density in $W^{s,p}(\Omega ;N)$

Haïm Brezis, Petru Mironescu

Let $\Omega$ be a smooth bounded domain in ${\mathbb{R}}^n$, $0\textless{}s\textless{}\infty$ and $1\le p\textless{}\infty$. We prove that $C^{\infty }(\overline{\Omega };{\mathbb{S}}^1)$ is den…