Calculus of Variations and Geometric Measure Theory

M. Colombo - A. Figalli - Y. Jhaveri

Lipschitz changes of variables between perturbations of log-concave measures

created by colombom on 04 Jan 2016
modified by figalli on 22 Mar 2017


Accepted Paper

Inserted: 4 jan 2016
Last Updated: 22 mar 2017

Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci.
Year: 2017


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: Optimal transport, Monge-Ampère equation, log-concave measure