 Green function of the Laplacian

ID: green-function-of-the-laplacian

Codex  0 Created 2026-09-24 Updated 2026-10-06

- \nabla^{2} \frac{1}{4 π ∣ x - x ^{'} ∣} = δ^{(3)} (x - x^{'}) .

Consequently the decaying solution of

- \nabla^{2} u = f

u (x) = \frac{1}{4 π} \int_{R^{3}} \frac{f ( x ^{'} )}{∣ x - x ^{'} ∣} d^{3} x^{'} .

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