Let $n\in\mathbb N$, let $U\subset\mathbb R^n$ be an [open set](/page/Open%20Set), let $1\le p<\infty$, and let $g\in W^{1,p}(U)$. Let $C_c^\infty(U)$ denote the [vector space](/page/Vector%20Space) of smooth real-valued functions with compact support in $U$, and define