Laplace equation

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

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

and the vector form is

$${\nabla }^2𝐀=0,$$

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

A function $f$ which satisfies Laplace’s equation is said to be harmonic. Since Laplace’s equation is linear, the superposition of any two solutions is also a solution.

Title	Laplace equation
Canonical name	LaplaceEquation
Date of creation	2013-03-22 13:09:11
Last modified on	2013-03-22 13:09:11
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	7
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 26B12
Synonym	Laplace differential equation
Related topic	PoissonsEquation
Related topic	ExampleOfSolvingTheHeatEquation
Defines	harmonic