Are there any way to prove maximum principle of harmonic functions without the mean value formula? In other words I would like to show $$ \max_{\overline{\Omega}}(f)=\max_{\partial \Omega}(f) $$ for a harmonic function $f$ on a bounded domain $\Omega$ without using the formula $$ f(x)=\frac{1}{V(B(x,r)}\int_{B(x,r)}f(z)dz. $$
Maximum principle of harmonic function without mean value formula
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harmonic-analysis