Calculus of Variations and Geometric Measure Theory

D. Cordero-Erausquin - A. Figalli

Regularity of monotone transport maps between unbounded domains

created by figalli on 03 Jun 2019


Accepted Paper

Inserted: 3 jun 2019
Last Updated: 3 jun 2019

Journal: Discrete Contin. Dyn. Syst.
Year: 2019


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.