Editing Elliptic partial differential equation (section)

{{Short description|Class of partial differential equations}}
{{Use American English|date = March 2019}}
{{Use mdy dates|date = March 2019}}

In [[mathematics]], an '''elliptic partial differential equation''' is a type of [[partial differential equation]] (PDE). In [[mathematical model]]ing, elliptic PDEs are frequently used to model [[steady state]]s, unlike [[parabolic PDE]] and [[hyperbolic PDE]] which generally model phenomena that change in time. The canonical examples of elliptic PDEs are [[Laplace's Equation]] and [[Poisson's Equation]]. Elliptic PDEs are also important in [[pure mathematics]], where they are fundamental to various fields of research such as [[differential geometry]] and [[optimal transport]].