Weak Formulation Of The Mtw Condition And Convexity Properties Of Potentials
METHODS AND APPLICATIONS OF ANALYSIS(2021)
Abstract
We simplify the geometric interpretation of the weak Ma-Trudinger-Wang condition for regularity in optimal transportation and provide a largely geometric proof of the global c-convexity of locally c-convex potentials when the cost function c is only assumed twice differentiable.
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Key words
cost function, convexity
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