Calculus of Variations and Geometric Measure Theory
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U. Bindini

Smoothing operators in multi-marginal Optimal Transport

created by bindini on 13 Feb 2019



Inserted: 13 feb 2019

Year: 2019

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.

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