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Let $\Omega \subseteq R^{n}$ bounded domain. I need to prove that for $u\in H^{2}(\Omega)\cap H^{1}_{0}(\Omega)$: \begin{equation} \|\nabla u\|_{L^{2}(\Omega)}^{2}\leq \|u\|_{L^{2}(\Omega)}\|\Delta u\...

I am studying the paper On some nonlinear elliptic problems for $p$-Laplacian in $\mathbb{R}^n$ by Abdelouahed El Khalil and Said El Manouni Mohammed Ouanan. I have a problem understanding one step ...