In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane ℝ2. 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 class of regular counterexamples to the optimality of this family of maps.
On deterministic solutions for multi-marginal optimal transport with Coulomb cost / Bindini, Ugo; De Pascale, Luigi; Kausamo, Anna. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 0:(2021), pp. 1-20. [10.3934/cpaa.2022015]
On deterministic solutions for multi-marginal optimal transport with Coulomb cost
De Pascale, Luigi;Kausamo, Anna
2021
Abstract
In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane ℝ2. 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 class of regular counterexamples to the optimality of this family of maps.File | Dimensione | Formato | |
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