Let \(k>\frac{n}{2}\) and \(U\subset \mathbb{R}^n\). Then for every \(u\in H^k_0(U)\) exists a constant \(C>0\) not depending on \(u\) such that
\begin{equation*} \lVert u\rVert_{L^\infty(U)}\le C\lVert u\rVert_{H^k_0(U)}. \end{equation*}Let \(k>\frac{n}{2}\) and \(U\subset \mathbb{R}^n\). Then for every \(u\in H^k_0(U)\) exists a constant \(C>0\) not depending on \(u\) such that
\begin{equation*} \lVert u\rVert_{L^\infty(U)}\le C\lVert u\rVert_{H^k_0(U)}. \end{equation*}