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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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