Template:Documentation/template page and Monge Ampere equation: Difference between pages

From nonlocal pde
(Difference between pages)
Jump to navigation Jump to search
imported>Plastikspork
m (Protected Template:Documentation/template page: Highly visible template: Will be used by Template:Documentation ([edit=sysop] (indefinite) [move=sysop] (indefinite)))
 
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...")
 
Line 1: Line 1:
{{#switch: {{SUBPAGENAME}}
The Monge-Ampere equation refers to
| sandbox
\[ \det D^2 u = f(x). \]
| testcases = {{BASEPAGENAME}}
The right hand side $f$ is always nonnegative. We look for a convex function $u$ which solves the equation.
| #default = {{PAGENAME}}
 
}}<noinclude>{{documentation|content=
The equation is uniformly elliptic when restricted to a subset of functions which are uniformly $C^{1,1}$ and strictly convex. Moreover, the operator
This subtemplate of {{tl|documentation}} is used to determine the template page name.
\[ MA(D^2 u) := \left( \det (D^2 u) \right)^{1/n} = \inf \{ a_{ij} \partial_{ij} u : \det \{a_{ij}\} = 1 \},\]
}}</noinclude>
is concave.
 
{{stub}}

Revision as of 16:46, 8 April 2015

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.

This article is a stub. You can help this nonlocal wiki by expanding it.