 Fundamental solution of the Laplace equation

ID: fundamental-solution-of-the-laplace-equation

Up to normalization and sign convention, a fundamental solution of the Laplace equation is

Φ (x) = ∣ x ∣^{2 - n}

for

n \geq 3

and

Φ (x) = lo g ∣ x ∣

for

n = 2

. It is harmonic away from the origin and satisfies

ΔΦ = c_{n} δ_{0}

distributionally.

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