Calculus of Variations and Geometric Measure Theory

U. Bindini

Smoothing operators in multi-marginal Optimal Transport

created by bindini on 13 Feb 2019
modified on 03 Aug 2021


Published Paper

Inserted: 13 feb 2019
Last Updated: 3 aug 2021

Journal: Math. Phys. Anal. Geom.
Volume: 23
Number: 2
Pages: 27
Year: 2020

ArXiv: 1901.07407 PDF


Given $N$ absolutely continuous probabilities $\rho_1, \dotsc, \rho_N$ over $\mathbb{R}^d$ which have Sobolev regularity, and given a transport plan $P$ with marginals $\rho_1, \dotsc, \rho_N$, we provide a universal technique to approximate $P$ with Sobolev regular transport plans with the same marginals. Moreover, we prove a sharp control of the energy and some continuity property of the approximating family.