# Laplace equation

From AMS Glossary

## Laplace equation

The elliptic partial differential equation where φ is a scalar function of position, and ∇

^{2}is the Laplacian operator.In rectangular Cartesian coordinates The Laplace equation is satisfied, for example, by the velocity potential in an irrotational flow, by gravitational potential in free space, by electrostatic potential in the steady flow of electric currents in solid conductors, and by the steady-state temperature distribution in solids. A solution of the Laplace equation is called an harmonic function.

*x*,*y*,*z*, this equation may be written*Compare*Poisson equation.