Obstructions to regularity in the classical Monge problem
Analysis of PDEs
2013-11-25 v1 Classical Analysis and ODEs
Functional Analysis
Optimization and Control
Probability
Abstract
We provide counterexamples to regularity of optimal maps in the classical Monge problem under various assumptions on the initial data. Our construction is based on a variant of the counterexample in \cite{LSW} to Lipschitz regularity of the monotone optimal map between smooth densities supported on convex domains.
Cite
@article{arxiv.1311.5868,
title = {Obstructions to regularity in the classical Monge problem},
author = {Maria Colombo and Emanuel Indrei},
journal= {arXiv preprint arXiv:1311.5868},
year = {2013}
}