My Math Forum L^p Louville Theorem

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 November 22nd, 2017, 10:34 AM #1 Newbie   Joined: Nov 2017 From: Uk Posts: 1 Thanks: 0 L^p Louville Theorem Have you got any ideas or can you help me in proving this theorem please ? Let $\displaystyle 1\leq p < \propto$, if $\displaystyle u \in C^{2}(R^{n})$, $\displaystyle \Delta u=0$ in $\displaystyle {R^{n}}$ and $\displaystyle u \in L^{p}(R^{n})$. so $\displaystyle \int_{R^{n}} \left | u(x) \right |^{p}\leq \propto$ Prove that: $\displaystyle u \equiv 0$ in $\displaystyle R^{n}$

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