Definition:Laplace's Equation

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

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


$\nabla^2 \psi = 0$

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

Source of Name

This entry was named for Pierre-Simon de Laplace.