Dictionary:Poisson’s equation

(pwa sonz’) In a space where the source density is ρ, the Laplacian of a potential U is

${\nabla }^{2}U=4\pi \rho K,$

where $\nabla$ is the operator del and K is a constant (the gravitational constant in the case of mass and gravitational potential). The constant 4π is deleted in some systems. In empty space where ρ=0, this becomes Laplace’s equation. Named for Simeon Denis Poisson (1781–1840), French mathematician.