The polar cone of the set of monotone maps

Cavalletti, Fabio; Westdickenberg, Michael

doi:10.1090/S0002-9939-2014-12332-X

The polar cone of the set of monotone maps
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by Fabio Cavalletti and Michael Westdickenberg PDF

Proc. Amer. Math. Soc. 143 (2015), 781-787 Request permission

Abstract:

We prove that every element of the polar cone to the closed convex cone of monotone transport maps can be represented as the divergence of a measure field taking values in the positive definite matrices.

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