Inserted: 4 jan 2016
Last Updated: 22 mar 2017
Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci.
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