Accepted Paper

Inserted: 4 jan 2016
Last Updated: 22 mar 2017

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

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

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