Lipschitz functions on $\mathbb R^n$ has bounded derivative

Question

A function $u:[a,b] \to \mathbb R$ is Lipschitz if and only if $u \in W^{1,\infty}([a,b])$.

Is it also true for $u:\Omega \to \mathbb R$ for $\Omega \subseteq \mathbb R^n$?