Open AccessOn deterministic solutions for multi-marginal optimal transport with Coulomb cost
Author(s) -
Ugo Bindini,
Luigi De Pascale,
Anna Kausamo
Publication year - 2022
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2022015
Subject(s) - counterexample , mathematics , coulomb , key (lock) , combinatorics , plane (geometry) , class (philosophy) , discrete mathematics , physics , computer science , geometry , quantum mechanics , artificial intelligence , computer security , electron
In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane \begin{document}$ \mathbb R^2 $\end{document} . 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.