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November 22nd, 2017, 11:34 AM   #1
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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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