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I'm trying to prove that if $\Omega$ is an open subset of $\mathbb{R}^n$ and $u$ a $C^2$ function then $$\lim_{r\to 0}\frac{2n}{r^2}\left(u(x)-\frac{1}{|\partial B_r(x)|}\int_{\partial B_r(x)}u(y)d\sigma_y\right)=-\Delta u(x).$$ I tried to use the representation formula on balls, but nothing came out of it..

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