Let $U\subset\mathbb R^n$ be a bounded Lipschitz domain, let $p>n$, and let $u\in W^{1,p}(U)$. Then $u$ has a representative in $C^{0,\gamma}(\overline{U})$ with \begin{align*} \gamma=1-\frac{n}{p}, \end{align*} and there exists $C>0$, depending on $U,n,p$, such that \begin{align*} \|u\|_{C^{0,\gamma}(\overline{U})}\le C\|u\|_{W^{1,p}(U)}. \end{align*}