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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 

Abstract

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.

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Résumé

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.

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