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arXiv · 1901.07407

Smoothing operators in multi-marginal Optimal Transport

Ugo Bindini
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Abstract

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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Ugo Bindini. 2019-01-22. Smoothing operators in multi-marginal Optimal Transport. https://doi.org/10.1007/s11040-020-09349-z

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