Δu = 0 on Ω. Mean-value property: u(x) = (1/V_r) ∫_{B_r(x)} u(y) dy for any ball. Implies maximum-principle. Conformally-invariant in 2D. Foundation of potential theory + harmonic analysis.
Δu = 0 on Ω. Mean-value property: u(x) = (1/V_r) ∫_{B_r(x)} u(y) dy for any ball. Implies maximum-principle. Conformally-invariant in 2D. Foundation of potential theory + harmonic analysis.