Lipschitz Changes of Variables between Perturbations of Log-concave Measures
Analysis of PDEs
2015-10-14 v1
Abstract
Extending a result of Caffarelli, we provide global Lipschitz changes of variables between compactly supported perturbations of log-concave measures. The result is based on a combination of ideas from optimal transportation theory and a new Pogorelov-type estimate. In the case of radially symmetric measures, Lipschitz changes of variables are obtained for a much broader class of perturbations.
Keywords
Cite
@article{arxiv.1510.03687,
title = {Lipschitz Changes of Variables between Perturbations of Log-concave Measures},
author = {Maria Colombo and Alessio Figalli and Yash Jhaveri},
journal= {arXiv preprint arXiv:1510.03687},
year = {2015}
}