We know that $W^{k,p}\hookrightarrow C^{k-\lfloor\frac{n}{p}\rfloor-1,\gamma}(\bar{\Omega})$ with $kp>n,\gamma=\lfloor\frac{n}{p}\rfloor+1-\frac{n}{p}$, where $n$ is the dimension of $\Omega$, $\Omega$ is a bounded domain in $\mathbb{R}^n$ with $C^1$ boundary.
From Wikipedia. This can also be seen in C.L.Evan's "*Partial Differential Equations*".

However, when $n/p$ is an integer, the theorem does not state anything more about $\gamma=1$. Is there any counterexample to $W^{k,p}\hookrightarrow C^{k-\frac{n}{p}-1,1}(\bar{\Omega})$ when $n/p$ is an integer? I don't know how to construct it, Thanks for your attention!.