I got the following question:
Let $\Omega \in \mathbb{R}^d, d \geq 2$ be any Lipschitz domain. Show that the embedding $W^{1,d}\left( \Omega \right) \hookrightarrow L^{\infty}\left( \Omega \right)$ does not hold.
Is it enough if I take a function, for example $u(x) = \ln \left(\frac{1}{|x|}\right)^\alpha$, and show that $u \in W^{1,d}$ and $u \notin L^{\infty}$?