Simple bound for $L^p$ norm

Question

Is there a bound for any $1<p<\infty$ or specifically $p=6$ such that

$$||u||_{L^{p}(U)}\leq C ||u||_{H^{1}(U)} $$

Where $U$ is an open bounded set of class $C^2$ in $\mathbb{R^3}$

and $H^{1}$ is the usual Sobolev norm.

Answer 1

It's is just the Sobolev embedding theorem when $p=6$.