Laplace equationLaplacesEquation2002-11-13 06:38:412006-11-13 22:58:45Definitionharmonic% this is the default PlanetMath preamble. as your knowledge
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\newcommand{\vnabla}{\nabla}The scalar form of \emph{Laplace's equation} is the partial differential equation $$\vnabla^2f = 0$$ and the vector form is $$\vnabla^2\vA = 0,$$where $\vnabla^2$ 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 \emph{harmonic}. Since Laplace's equation is linear, the superposition of any two solutions is also a solution.