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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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