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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

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  • $\begingroup$ Did you mean to say that $f$ is sequentially weakly lower semicontinous? $\endgroup$ – BigbearZzz May 19 at 23:27
  • $\begingroup$ Yes this is what i meant $\endgroup$ – Mono May 20 at 14:48
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The functional is continuous and convex, hence, sequentially weakly lower semicontinuous.

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