Poisson’s equation is an elliptic partial differential equation used widely in theoretical physics.
For example, the solution to Poisson’s equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate electrostatic or gravitational (force) field.
It is a generalization of Laplace’s equation, which is also frequently seen in physics. The equation is named after French mathematician and physicist Siméon Denis Poisson.