imported>Luis at 21:47, 8 April 2015

2015-04-08T21:47:36Z

← Older revision		Revision as of 16:47, 8 April 2015
Line 1:		Line 1:
	The Monge-Ampere equation refers to		The Monge-Ampere equation refers to
	\[ \det D^2 u = f(x). \]		\[ \det D^2 u = f(x). \]
	The right hand side $f$ is always nonnegative. ~~We look for a convex~~ function $u$ ~~which solves the equation~~.		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		The equation is uniformly elliptic when restricted to a subset of functions which are uniformly $C^{1,1}$ and strictly convex. Moreover, the operator

imported>Luis: Created page with "The Monge-Ampere equation refers to \[ \det D^2 u = f(x). \] The right hand side $f$ is always nonnegative. We look for a convex function $u$ which solves the equation. The equ..."

2015-04-08T21:46:52Z

Created page with "The Monge-Ampere equation refers to \[ \det D^2 u = f(x). \] The right hand side $f$ is always nonnegative. We look for a convex function $u$ which solves the equation. The equ..."

New page

The Monge-Ampere equation refers to
\[ \det D^2 u = f(x). \]
The right hand side $f$ is always nonnegative. We look for a convex function $u$ which solves the equation.

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.

{{stub}}

Monge Ampere equation - Revision history

imported>Luis at 21:47, 8 April 2015

imported>Luis: Created page with "The Monge-Ampere equation refers to \[ \det D^2 u = f(x). \] The right hand side $f$ is always nonnegative. We look for a convex function $u$ which solves the equation. The equ..."