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Let $\Omega$ be a bounded domain with Lipschitz border. We define $G:W^{1,p} \rightarrow\mathbb{R}$ by $$G(u)=\int_{\partial\Omega}|u|^pd\sigma.$$ How can I show that $(G'(u),h)=\int_{\partial\Omega}|u|^{p-2}u \, dh\, \sigma$ for all $h\in W^{1,p}(\Omega)$?

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