Can anyone give me a hint to show the following?

Let $m$ be a positive integer and $u : \mathbb{R}^{n} \rightarrow \mathbb{R}$ be a harmonic function. If $u(x) = O(\left|x \right|)^m$ when $\left|x \right| \to \infty$, show that $u$ is polynomial of degree at most $m$.

Any clue will be great.


  • 2
    $\begingroup$ You mean "a polynomial of degree at most $m$"? $\endgroup$ – Teddan the Terran Sep 28 at 16:10
  • $\begingroup$ Do you know an/the interior estimate for harmonic functions? $\endgroup$ – hal4math Sep 28 at 16:19
  • $\begingroup$ yes, thanks. @TeddantheTerran $\endgroup$ – Lica Sep 30 at 22:38
  • $\begingroup$ Do not know @hal4math $\endgroup$ – Lica Sep 30 at 22:40

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