Hölder regularity of optimal mappings in optimal transportation

Jiakun Liu
April 2009
Calculus of Variations & Partial Differential Equations;Apr2009, Vol. 34 Issue 4, p435
Academic Journal
It is known that optimal mappings in optimal transportation problems are uniquely determined by corresponding potential functions. In this paper we prove various local properties of potential functions. In particular we obtain the C1, α regularity of potential functions with optimal exponent α, which improves previous regularity results of Loeper.


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