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# Laplace equation

The scalar form of *Laplace’s equation* is the partial differential equation

$\nabla^{2}f=0$ |

and the vector form is

$\nabla^{2}\mathbf{A}=0,$ |

where $\nabla^{2}$ is the Laplacian. It is a special case of the Helmholtz differential equation with $k=0.$

Defines:

harmonic

Related:

PoissonsEquation, ExampleOfSolvingTheHeatEquation

Synonym:

Laplace differential equation

Type of Math Object:

Definition

Major Section:

Reference

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26B12*no label found*

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## Corrections

two things by rmilson ✓

suggestion by igor ✓

del A^2? by matte ✘

emphasis on defined terms by Mathprof ✓

suggestion by igor ✓

del A^2? by matte ✘

emphasis on defined terms by Mathprof ✓