Laplace equation

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


and the vector form is


where 2 is the Laplacian. It is a special case of the Helmholtz differential equationMathworldPlanetmath 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