Continuity and Estimates for Multimarginal Optimal Transportation Problems with Singular Costs

We consider some repulsive multimarginal optimal transportation problems which include, as a particular case, the Coulomb cost. We prove a regularity property of the minimizers (optimal transportation plan) from which we deduce existence and some basic regularity of a maximizer for the dual problem...

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Bibliographic Details
Published in:Applied mathematics & optimization 2018-08, Vol.78 (1), p.185-200
Main Authors: Buttazzo, Giuseppe, Champion, Thierry, De Pascale, Luigi
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Continuity
Control
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimization and Control
Regularity
Simulation
Systems Theory
Theoretical
Transportation
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Summary:We consider some repulsive multimarginal optimal transportation problems which include, as a particular case, the Coulomb cost. We prove a regularity property of the minimizers (optimal transportation plan) from which we deduce existence and some basic regularity of a maximizer for the dual problem (Kantorovich potential). This is then applied to obtain some estimates of the cost and to the study of continuity properties.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-017-9403-7