# 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 $k=0.$

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.

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