Laplace equation

It belongs to the famous equations.
In the 3D case is

\frac{\partial^{2} f}{\partial x^{2}} + \frac{\partial^{2} f}{\partial y^{2}} + \frac{\partial^{2} f}{\partial z^{2}} = 0.

The operator

\frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial y^{2}} + \frac{\partial^{2}}{\partial z^{2}}

is called the Laplacian operator, and is usually denoted by $Δ$ or $\nabla^{2}$ .

The solutions are called harmonic functions.