How to prove usign partitions of unity and flattening out $\partial U$ the statement (6) below? 
This theorem is about trace-zero functions in $W^{1,p}(U)$, where $U \subset \mathbb{R^n}$ is a bounded domain with boundary $C^1$. I know that I need to use the definition of boundary $C^1$, but I don't know how.We initially assume that $u \in W^{1,p}(U)$.