# Monge Ampere equation

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The Monge-Ampere equation refers to $\det D^2 u = f(x).$ The right hand side $f$ is always nonnegative. The unknown function $u$ should be convex.
The equation is uniformly elliptic when restricted to a subset of functions which are uniformly $C^{1,1}$ and strictly convex. Moreover, the operator $MA(D^2 u) := \left( \det (D^2 u) \right)^{1/n} = \inf \{ a_{ij} \partial_{ij} u : \det \{a_{ij}\} = 1 \},$ is concave.