Laplace’s Equation

For a function $f(x,y)$ the equation

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

is called Laplace’s equation. This is also written as:

$${\nabla }^{2}f(x,y)=0$$

Functions that satisfy Laplace’s equation are called harmonic functions.