In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane ${mathbb R}^2$. The key question is the optimality of the so-called Seidl map, first disproved by Colombo and Stra. We generalize the partial positive result obtained by Colombo and Stra and give a necessary and sufficient condition for the radial Coulomb cost to coincide with a much simpler cost that corresponds to the situation where all three particles are aligned. Moreover, we produce an infinite family of regular counterexamples to the optimality of Seidl-type maps.

On Seidl-type maps for multi-marginal optimal transport with Coulomb cost / Ugo Bindini; Luigi De Pascale; Anna Kausamo. - ELETTRONICO. - (2020), pp. 1-25.

On Seidl-type maps for multi-marginal optimal transport with Coulomb cost

Luigi De Pascale
;
2020

Abstract

In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane ${mathbb R}^2$. The key question is the optimality of the so-called Seidl map, first disproved by Colombo and Stra. We generalize the partial positive result obtained by Colombo and Stra and give a necessary and sufficient condition for the radial Coulomb cost to coincide with a much simpler cost that corresponds to the situation where all three particles are aligned. Moreover, we produce an infinite family of regular counterexamples to the optimality of Seidl-type maps.
Goal 9: Industry, Innovation, and Infrastructure
Ugo Bindini; Luigi De Pascale; Anna Kausamo
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2158/1217940
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