Have you got any ideas or can you help me in proving this theorem please ?


Let $\displaystyle 1\leq p\leq \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 $\displaystyle R^{n}$