Regularity of monotone transport maps between unbounded domains

Dario Cordero-Erausquin, Alessio Figalli

Published 2019-02-20Version 1

The regularity of monotone transport maps plays an important role in several applications to PDE and geometry. Unfortunately, the classical statements on this subject are restricted to the case when the measures are compactly supported. In this note we show that, in several situations of interest, one can to ensure the regularity of monotone maps even if the measures may have unbounded supports.