Definition:Laplace's Equation

Equation
Laplace's equation is a second order PDE of the form:


 * $\dfrac {\partial^2 \psi} {\partial x^2} + \dfrac {\partial^2 \psi} {\partial y^2} + \dfrac {\partial^2 \psi} {\partial z^2} = 0$

or:
 * $\nabla^2 \psi = 0$

where $\nabla^2$ denotes the Laplacian operator.

Also known as
Laplace's equation is also known as the equation of continuity.

Some sources render it as Laplace equation.

Also see

 * Definition:Poisson's Differential Equation, of which Laplace's equation can be considered a special case.


 * Solution to Laplace's Equation