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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.
Multi-marginal optimal transport: theory and applications
Brendan Pass · 1901
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Uniformly convex spaces
James A Clarkson · 1936
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Density functionals for coulomb systems
Elliott H. Lieb · 2002
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Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2008
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Codina Cotar, Gero Friesecke, and Claudia Klüppelberg · 2018
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Semi-classical limit of the levy–lieb functional in density functional theory
Mathieu Lewin · 2018
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