I have a question about Sobolev spaces

Let $U$ be a bounded Lipschitz domain of $\mathbb{R}^{d}$. $H^{1}(U)$ denotes the first order $L^2$-Sobolev space on $U$ with Neumann boundary condition.

It is well known that there exists a bounded linear operator \begin{equation*} T:H^{1}(U) \to L^{2}(\partial U;\mathcal{H}^{d-1}) \end{equation*} such that $Tf=f$ on $\partial U$ for all $f\in H^{1}(U)\cap C(\bar{U})$. Here $\mathcal{H}^{d-1}$ denotes the $d-1$ Hausdorff measure.

My question

Is there generalization of this theorem? Even if $U$ is not Lipschitz domain, trace operator $T$ exist?

If you know related results, please let me know.