Assume $\Omega \subset L_d$, for some $d > 0$. Then, for all $u \in W^{1,q}_0(\Omega)$ $1 \leq q \leq \infty$ , $\left \|u \right \|_p \leq (d/2)\left \| \nabla u \right \|_p$. Prove that the Inequality fails, in general, if $\Omega$ is not contained in some layer $L_d$. Suppose, for instance, $\Omega$$R^n$

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    $\begingroup$ What is $L_d$?? $\endgroup$ – Jeff Jun 15 at 20:10

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