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The polar cone of the set of monotone maps


Authors: Fabio Cavalletti and Michael Westdickenberg
Journal: Proc. Amer. Math. Soc. 143 (2015), 781-787
MSC (2010): Primary 49Q20
DOI: https://doi.org/10.1090/S0002-9939-2014-12332-X
Published electronically: October 15, 2014
MathSciNet review: 3283664
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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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Additional Information

Fabio Cavalletti
Affiliation: Lehrstuhl für Mathematik (Analysis), RWTH Aachen University, Templergraben 55, D-52062 Aachen, Germany
Email: cavalletti@instmath.rwth-aachen.de

Michael Westdickenberg
Affiliation: Lehrstuhl für Mathematik (Analysis), RWTH Aachen University, Templergraben 55, D-52062 Aachen, Germany
Email: mwest@instmath.rwth-aachen.de

DOI: https://doi.org/10.1090/S0002-9939-2014-12332-X
Keywords: Optimal transport, polar cone
Received by editor(s): May 10, 2013
Received by editor(s) in revised form: June 3, 2013
Published electronically: October 15, 2014
Communicated by: Walter Craig
Article copyright: © Copyright 2014 American Mathematical Society

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