# Sequentially lower semicontinuity

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

• Did you mean to say that $f$ is sequentially weakly lower semicontinous? – BigbearZzz May 19 at 23:27
• Yes this is what i meant – Mono May 20 at 14:48