6533b86ffe1ef96bd12cd333
RESEARCH PRODUCT
On deterministic solutions for multi-marginal optimal transport with Coulomb cost
Ugo BindiniLuigi De PascaleAnna Kausamosubject
Multimarginal optimal transportation Monge-Kantorovich problem Duality theory Coulomb cost Density Functional Theory.Applied MathematicstiheysfunktionaaliteoriaFOS: Physical sciencesMonge-Kantorovich problemduality theoryvariaatiolaskentaMathematical Physics (math-ph)General MedicineDensity Functional Theory.matemaattinen optimointimultimarginal optimal transportation49J45 49N15 49K30Mathematics - Analysis of PDEsOptimization and Control (math.OC)Coulomb costFOS: MathematicsMathematics - Optimization and ControlMathematical PhysicsAnalysisAnalysis of PDEs (math.AP)description
In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane $\R^2$. 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 class of regular counterexamples to the optimality of this family of maps.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-01-01 |