2020/11/10 by Ugo Bindini, Bindini, Ugo, Luigi De Pascale +3
Mathematics · #49J45 #49K30 #49N15 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2011.05063
openalex publication_date 2020/11/10 · openalex created_date 2023/02/11 · openalex updated_date 2026/07/28
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.