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How to show the following statement? Let $\Omega$ be a bounded Lipschitz convex domain. If $u$ satisfies the following equation, $$ -\Delta u - k^2 u = f \quad\mbox{ in }\Omega \\ \nabla u \...

Let $d\in\mathbb N$ $\Lambda\subseteq\mathbb R^d$ be bounded and open $f\in L^2(\Lambda,\mathbb R^d)$ $u\in H_0^1(\Lambda,\mathbb R^d)$ with $$-\langle\nabla\phi,\nabla u\rangle_{L^2(\Lambda,\:\...