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Marginals with Finite Repulsive Cost

Part of: Existence theories Optimality conditions

Published online by Cambridge University Press:  07 May 2019

Ugo Bindini
Ugo Bindini*
Affiliation:
Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56127 Pisa, Italy Email: [email protected]
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Abstract

We consider a multimarginal transport problem with repulsive cost, where the marginals are all equal to a fixed probability $\unicode[STIX]{x1D70C}\in {\mathcal{P}}(\mathbb{R}^{d})$. We prove that, if the concentration of $\unicode[STIX]{x1D70C}$ is less than $1/N$, then the problem has a solution of finite cost. The result is sharp, in the sense that there exists $\unicode[STIX]{x1D70C}$ with concentration $1/N$ for which the cost is infinite.

Keywords

multi-marginaloptimal transportrepulsive cost

MSC classification

Primary: 49J10: Free problems in two or more independent variables
Secondary: 49K10: Free problems in two or more independent variables
Type
Article
Information
Canadian Journal of Mathematics , Volume 72 , Issue 2 , April 2020 , pp. 373 - 391
Copyright
© Canadian Mathematical Society 2018

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