Continuity and estimates for multimarginal optimal transportation problems with singular costs
Optimization and Control
2016-09-01 v1
Abstract
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.
Cite
@article{arxiv.1608.08780,
title = {Continuity and estimates for multimarginal optimal transportation problems with singular costs},
author = {Giuseppe Buttazzo and Thierry Champion and Luigi De Pascale},
journal= {arXiv preprint arXiv:1608.08780},
year = {2016}
}