I was studying Evans book (Partial Differential Equations) and in page 279 he use the fact that if a sequence $u_{n}\in L^{\infty}(\mathbb{R}^{n})$ is such that $\|u_{n}\|_{\infty}\leq C$ $C$ constant, then there exist $u\in L^{\infty}(\mathbb{R}^{n})$ such that a subsequence of $u_{n}$ converges weakly in $L^{2}_{Loc}(\mathbb{R}^{n})$ to $u$.
Now my question is: If $\Omega$ is a bounded domain, then $L^{p}(\Omega)\hookrightarrow L^{q}(\Omega)$, where $1\leq q and "$\hookrightarrow$" stands for compact immersion? The answer of the question or any reference is appreciate. Thanks