Strict convexity and C1,a regularity of potential functions in optimal transportation under condition A3w
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 , Loeper , Trudinger and Wang  for costs satisfying the condition (A3). For costs satisfying the condition (A3w), the results have also been proved by Figalli, Kim, and McCann , assuming that the initial and target domains are uniformly c-convex, see also...[Show more]
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|Source:||Journal of Differential Equations|
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