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Strict convexity and C1,a regularity of potential functions in optimal transportation under condition A3w

Chen, Shibing; Wang, Xu-Jia


In this paper we prove the strict c-convexity and the C1,α regularity for potential functions in optimal transportation under condition (A3w). These results were obtained by Caffarelli [1,3,4] for the cost c(x, y)=|x-y|2, by Liu [11], Loeper [15], Trudinger and Wang [20] for costs satisfying the condition (A3). For costs satisfying the condition (A3w), the results have also been proved by Figalli, Kim, and McCann [6], assuming that the initial and target domains are uniformly c-convex, see also...[Show more]

CollectionsANU Research Publications
Date published: 2016
Type: Journal article
Source: Journal of Differential Equations
DOI: 10.1016/j.jde.2015.09.047


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