The scalar form of 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 harmonic. Since Laplace's equation is linear, the superposition of any two solutions is also a solution.