Let $\Omega\subset \mathbb{R}^n$ be open and bounded. Also let
$W^{1,2}(\Omega)=\left\{u \in L^{2}(\Omega)|\,\, \forall \alpha \in \mathbb{N}^{n}:|\alpha| \leq 1\,\, \exists \,D^{\alpha} u \in L^{p}(\Omega)\right\}$
denote the sobolev space.
Futher let $u_n\rightarrow u$ converge weakly in $W^{1,2}(\Omega)$. In the lecture it is sad that this implies $u_n\rightarrow u$ strongly in $L^2(\Omega)$. Does anyone have an explaination?