6 papers
A remark on the geometric interpretation of the A3w condition from optimal transport
Cale Rankin
We provide a geometric interpretation of the well known A3w condition for regularity of optimal transport maps.
First and second derivative Hölder estimates for generated Jacobian equations
Cale Rankin
We prove two Hölder regularity results for solutions of generated Jacobian equations. First, that under the A3 condition and the assumption of nonnegative valued data solutio…
Regularity and uniqueness results for generated Jacobian equations
Cale Rankin
This is a PhD thesis about generated Jacobian equations; our purpose is twofold. First, we provide an introduction to these equations, whilst, at the same time, collating some resu…
Strict -convexity for generated Jacobian equations with applications to global regularity
Cale Rankin
This article has two purposes. The first is to prove solutions of the second boundary value problem for generated Jacobian equations are strictly -convex. The second is to prove…
Strict convexity and regularity of solutions to generated Jacobian equations in dimension two
Cale Rankin
We present a proof of strict -convexity in 2D for solutions of generated Jacobian equations with a -Monge-Ampère measure bounded away from 0. Subsequently this implies …
Distinct solutions to generated Jacobian equations cannot intersect
Cale Rankin
We prove that if two solutions of the second boundary value problem for the generated Jacobian equation intersect in then they are the same solution. In addition w…