The solutions of the Laplace equation $\Delta f =0$ on a domain $D\subset \mathbb{R}^n$ are known as *harmonic functions*.
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Limit involving the laplacian
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 ...
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Why are harmonic functions called harmonic functions?
Are they related to harmonic series in any way? Or something else? Wikipedia didn't help.
