The Plateau problem from the perspective of optimal transport

Brezis, Haim; Mironescu, Petru

doi:10.1016/j.crma.2019.07.007

Partial differential equations

The Plateau problem from the perspective of optimal transport
[Le problème de Plateau vu dans la perspective du transport optimal]

Présenté par : Haïm Brézis

Brezis, Haim ^1,^2,³ ; Mironescu, Petru ⁴

¹ Department of Mathematics, Rutgers University, USA
² Departments of Mathematics and Computer Science, Technion – I.I.T., 32 000 Haifa, Israel
³ Sorbonne Universités, UPMC Université Paris-6, UMR 7598, Laboratoire Jacques-Louis-Lions, 75005, Paris, France
⁴ Univ Lyon, Université Claude-Bernard – Lyon-1, CNRS UMR 5208, Institut Camille-Jordan, 69622 Villeurbanne, France

Comptes Rendus. Mathématique, Tome 357 (2019) no. 7, pp. 597-612.

Résumé
Abstract

Le transport optimal, ainsi que les surfaces minimales, ont été abondamment étudiés au cours de ces dernières décennies. Nous mettons en évidence une analogie surprenante, au niveau méthodologique, entre l'approche de Kantorovich pour le problème de Monge et la minimisation de l'aire dans des problèmes géométriques de type Plateau étudiés par Federer.

Both optimal transport and minimal surfaces have received much attention in recent years. We show that the methodology introduced by Kantorovich on the Monge problem can, surprisingly, be adapted to questions involving least area, e.g., Plateau-type problems as investigated by Federer.

Reçu le : 2019-07-30
Accepté le : 2019-07-30
Publié le : 2019-07-01

DOI : 10.1016/j.crma.2019.07.007

Affiliations des auteurs :

Brezis, Haim ^{1, 2, 3} ; Mironescu, Petru ⁴

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Brezis, Haim; Mironescu, Petru. The Plateau problem from the perspective of optimal transport. Comptes Rendus. Mathématique, Tome 357 (2019) no. 7, pp. 597-612. doi : 10.1016/j.crma.2019.07.007. http://www.numdam.org/articles/10.1016/j.crma.2019.07.007/

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