In mathematics, a (real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function "u" of two variables "x","y" is of Monge–Ampère type if it is linear in the determinant of the Hessian matrix of "u" and in the second-order partial derivatives of "u". The independent variables ("x","y") vary over a given domain "D" of R2. The term also applies to analogous equations with "n" independent variables. The most complete results so far have been obtained when the equation is elliptic.