Sequentially lower semicontinuity

Question

Let $\Omega$ be a bounded open set with lipschitz boundary, How can we show that the functional defined by $f:W^{1,p}\rightarrow\mathbb{R}$ $f(u)=\int_{\Omega}|Du|_{\mathbb{R}^N}^p$ is sequentialy weakly lower semicontinous

Answer 1

The functional is continuous and convex, hence, sequentially weakly lower semicontinuous.