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Comptes Rendus Mathématique
Volume 353, n° 12
pages 1099-1104 (décembre 2015)
Doi : 10.1016/j.crma.2015.09.015
Received : 4 August 2015 ;  accepted : 18 September 2015
Optimal transport of closed differential forms for convex costs
Transport optimal des formes fermées pour des coûts convexes

Bernard Dacorogna a , Wilfrid Gangbo b , Olivier Kneuss c
a Section de Mathématiques, EPFL, CH-1015 Lausanne, Switzerland 
b School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA 
c Department of Mathematics, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil 


Let   be convex and   be a bounded domain. Let   and   be two closed k -forms on Ω satisfying appropriate boundary conditions. We discuss the minimization of   over a subset of  -forms A on Ω such that  , and its connection with a transport of symplectic forms. Section 3 mainly serves as a step toward Section 4, which is richer, as it connects to variational problems with multiple minimizers.

The full text of this article is available in PDF format.

Soient   une fonction convexe et   un domaine borné. Soient   et   des k -formes fermées sur Ω satisfaisant des conditions de bord appropriées. Nous nous intéressons à la minimisation de   sur l'ensemble des  -formes A telles que  , ainsi que sa relation à un problème de transport des formes symplectiques. La Section 3 sert d'étape intermédiaire vers la Section 4, qui est plus riche, car reliée à des problèmes variationnels avec une multitude de minimiseurs.

The full text of this article is available in PDF format.

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