In Partial Differential Equation by Lawerence Evan p284 there is this theorem stated:

Let $U$ be a bounded open subset of $\mathbb{R}^n$ with $C^1$ boundary. Suppose $u\in W^{k,p}$ then if $k>n/p$ we have

$ u\in C^{\alpha, \gamma}(\overline{U}) $ where $\alpha = k-\left[n/p\right]-1$ and $\gamma = \left[n/p\right]+1-n/p$ if $n/p$ is not an integer and any $0<\gamma<1$ if $n/p\in\mathbb{N}$.

I have two questions:

- Does this result extend to $U$ being an open subset with only Lipschitz boundary?

2.Does the result also holds $k\not\in\mathbb{N}$? The author doesn't mention anyway that $k$ should be an integer but I just wanted to check.

Thank you in advance.