Suppose $s∈(0,1)$, $D$ is an open set in $\mathbb{R}^d$. Define $$ H^s=(1−\Delta)^{-s/2}L^2(\mathbb{R}^d), $$ $$ H^s_D=\{f\in H^s:f=0 \ a.e.\ on\ D^c\}. $$ Q: Is $C^\infty_c(D)$ dense in $H^s_D$(with norm $\|\cdot\|_{H^s}$) for any open set $D$?

Is there any element reference?