On the local theory of prescribed Jacobian equations

By Neil S. Trudinger. 2012

61 citations recorded by the source corpus.

We develop the fundamentals of a local regularity theory for pre- scribed Jacobian equations which extend the corresponding results for optimal transportation equations. In this theory the cost function is extended to a generating function through dependence on an additional scalar variable. In particular we recover in this generality the local regularity theory for poten- tials of Ma, Trudinger and Wang, along with the subsequent development of the underlying convexity theory.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/15cc3036dd9a65a03066c25f9c690700210980f7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Oblique boundary value problems for augmented Hessian equations I (2015, background): “From geometric optics we have the example coming from the reflection of a parallel beam to a flat target, [38, 24],”
On the Dirichlet problem for Monge-Ampère type equations (2013, background): “1 also extends to embrace prescribed Jacobian equations with mappings Y determined by generating functions as in [25].”
The Monge–Ampère equation and its link to optimal transportation (2013, background): “ case described in this note corresponds to the case r xc(x;T(x;p)) = p; that is T(x;p) = c-exp x (p) (compare with Section 3.4). Motivated by problems arising in geometric optics, Trudinger began in [104, 105] a systematic study of equations of the form (5.1)-(5.2) in the particular when Tis obtain”