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math.AP2022
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.
math.AP2022
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…
math.AP2022
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…