We provide sharp conditions for the finiteness and the continuity of multimarginal optimal transport with repulsive cost, expressed in terms of a suitable concentration property of the measure. To achieve this result, we analyze the Kantorovich potentials of the optimal plans, and we estimate the distance of any optimal plan from the regions where the cost is infinite.
Continuity of Multimarginal Optimal Transport with Repulsive Cost
Di Marino S;
2019-01-01
Abstract
We provide sharp conditions for the finiteness and the continuity of multimarginal optimal transport with repulsive cost, expressed in terms of a suitable concentration property of the measure. To achieve this result, we analyze the Kantorovich potentials of the optimal plans, and we estimate the distance of any optimal plan from the regions where the cost is infinite.
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