In the setting of the optimal transportation problem we provide some conditions which ensure the existence and the uniqueness of the optimal map in the case of cost functions satisfying mild regularity hypothesis and no convexity or concavity assumptions.
Uniqueness and non uniqueness of optimal maps in mass transport problem with not strictly convex cost
VAN DER PUTTEN, ROBERTUS
2010-01-01
Abstract
In the setting of the optimal transportation problem we provide some conditions which ensure the existence and the uniqueness of the optimal map in the case of cost functions satisfying mild regularity hypothesis and no convexity or concavity assumptions.
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