If $\Omega$ is an open Lipschitz domain with bounded boundary then their exists a continuous operator $E: W^{s,p}(\Omega) \rightarrow W^{s,p}(\mathbb{R}^d)$ where $s\in (0,1)$ such that $Eu=u$ on $\Omega$.

A similar result holds for integer order Sobolev spaces.

But in case of integer order sobolev spaces one always has the existence of a continous extension operator $E: W_0^{k,p}(\Omega) \rightarrow W^{k,p}(\mathbb{R}^d)$ regardless of the regularity of $\Omega$ e.g. the zero extension.

> My question is, if $\Omega$ is only open, do we also have the existence
> of a continuous extension operator 
> 
> $$E: W_0^{s,p}(\Omega) \rightarrow W^{s,p}(\mathbb{R}^d) \text{ where } s\in(0,1)$$

If yes, can someone suggest literature where this is mentioned?

Honestly, I don't want to bother trying to prove it myself, or rather, I would like to have at least assurance that this is true first.

By the way the space $W^{s,p}_0(\Omega)$ is defined as the closure of $C_0^\infty(\Omega)$ wrt. to the norm $\|u\|_{W^{s,p}}^p:=|\cdot|_{s,p,\Omega}^p+\|\cdot\|_{L^p(\Omega)}^p$, where $|u|_{s,p,\Omega}^p:=\int_{\Omega \times \Omega} \frac{|u(x)-u(y)|^p}{|x-y|^{d+sp}}d(x,y)$ is the Gagliardo seminorm.

My thought on this:
As in the integer-order case one might consider the extension by zero of $u \in W^{s,p}_0(\Omega)$ and try to show that this extension satsifies the above requirement. Yet, we have that 

$\|Eu\|_{W^{s,p}(\mathbb{R}^d)}^p=\|u\|_{W^{s,p}(\Omega)}^p+2\int_U \left(\int_{\mathbb{R}^d\setminus U} \frac{1}{|x-y|^{s+sp}} dy \right)|u(x)|^pdx$.

If this could be further estimated by $C\|u\|_{W^{s,p}}$ for some constant $C$ then the extension by zero would be continuous from $W^{s,p}_0(\Omega)$ to $W^{s,p}(\mathbb{R}^d)$.