Density of smooth functions in a Sobolev space
= Density of smooth functions in a Sobolev space
For every open set $U\subseteq\mathbb R^n$, smooth functions in $U$ are dense in $W^{1,p}(U)$ for $1\leq p<\infty$. Near a flat boundary, one may first translate the function into the domain and then apply a <mollifier>.