# Dictionary:Poisson’s equation

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

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

where ${\displaystyle \nabla }$ 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.