Optimal Transport and the Monge Ampère equation: Difference between revisions
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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. | 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. | ||
== | == Deriving the Monge Ampère equation from Monge's Problem == | ||
==References== | ==References== | ||
Revision as of 23:41, 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.