Equality between Monge and Kantorovich multimarginal problems with Coulomb cost

DOI10.1007/s10231-013-0376-0zbMath1315.49021OpenAlexW2068098209MaRDI QIDQ2340916

Simone Di Marino, Maria Colombo

Publication date: 21 April 2015

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: http://link.springer.com/10.1007/s10231-013-0376-0

zbMATH Keywords

optimal transportMonge-Kantorovich problemmultimarginal problem

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Optimal stochastic control (93E20) Duality theory (optimization) (49N15) Measures and integrals in product spaces (28A35) Integration and disintegration of measures (28A50) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items (11)

On deterministic solutions for multi-marginal optimal transport with Coulomb cost ⋮ On ergodic decompositions related to the Kantorovich problem ⋮ Continuity and estimates for multimarginal optimal transportation problems with singular costs ⋮ Universal diagonal estimates for minimizers of the Levy-Lieb functional ⋮ Optimal mass transport and symmetric representations of their cost functions ⋮ Symmetric Monge-Kantorovich problems and polar decompositions of vector fields ⋮ Infinite-body optimal transport with Coulomb cost ⋮ Semi-classical limit of the Levy-Lieb functional in density functional theory ⋮ Marginals with Finite Repulsive Cost ⋮ Continuity of Multimarginal Optimal Transport with Repulsive Cost ⋮ On c-cyclical monotonicity for optimal transport problem with Coulomb cost

Cites Work

• Remarks on multi-marginal symmetric Monge-Kantorovich problems
• Symmetric Monge-Kantorovich problems and polar decompositions of vector fields
• On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation
• Mass transportation problems. Vol. 1: Theory. Vol. 2: Applications
• Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope
• Uniqueness and Monge Solutions in the Multimarginal Optimal Transportation Problem
• Optimal maps for the multidimensional Monge-Kantorovich problem
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral
• Density Functional Theory and Optimal Transportation with Coulomb Cost
• Multimarginal Optimal Transport Maps for One–dimensional Repulsive Costs
• Optimal Transport
• Unnamed Item

This page was built for publication: Equality between Monge and Kantorovich multimarginal problems with Coulomb cost