Optimal Transport and the Monge Ampère equation: Difference between revisions

From Optimal Transport Wiki
Jump to navigation Jump to search
No edit summary
No edit summary
Line 1: Line 1:
The Monge Ampère equation<ref name="Santambrogio" />
The Monge Ampère equation<ref name="Santambrogio" /> is an nonlinear second-order elliptic partial differential equation. Given sufficient conditions on an optimal transport problem, the Monge Ampère equation defines a change of variables formula for the pushforward of a transport map. In particular, the Monge Ampère equation applies to a variant of the [[Monge Problem]] where the cost function is quadratic.


==References==
==References==

Revision as of 23:36, 8 May 2020

The Monge Ampère equation[1] is an nonlinear second-order elliptic partial differential equation. Given sufficient conditions on an optimal transport problem, the Monge Ampère equation defines a change of variables formula for the pushforward of a transport map. In particular, the Monge Ampère equation applies to a variant of the Monge Problem where the cost function is quadratic.

References

  1. ↑ F. Santambrogio, Optimal Transport for Applied Mathematicians, Chapter 1.
Retrieved from "http://www.otwiki.xyz/index.php?title=Optimal_Transport_and_the_Monge_Ampère_equation&oldid=221"