A Modica–Mortola approximation for branched transport

Filippo Santambrogio

doi:10.1016/j.crma.2010.07.016

Calculus of Variations

A Modica–Mortola approximation for branched transport

Presented by: Jean-Michel Bony

Filippo Santambrogio ¹

¹ CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, place de Lattre de Tassigny, 75775 Paris cedex 16, France

Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 941-945.

Abstract
Résumé

The $M^{α}$ energy which is minimized in branched transport problems among singular 1-dimensional rectifiable vector measures with prescribed divergence is approximated by means of a sequence of elliptic energies, defined on more regular vector fields. The procedure recalls that of Modica–Mortola to approximate the perimeter, and the double-well potential is replaced by a concave power.

L'énergie $M^{α}$ qui est minimisée dans les problèmes de transport branché parmi les mesures vectorielles (singulières et supportées sur des ensembles rectifiables de dimension 1) à divergence fixée est approximée par une suite d'énergies elliptiques, définies sur des champs de vecteurs plus réguliers. La procédure rappelle celle de Modica et Mortola pour le périmètre, et le potentiel à double puits est remplacé par une puissance concave.

Received: 2010-06-14
Accepted: 2010-07-16
Published online: 2010-07-31

DOI: 10.1016/j.crma.2010.07.016

Author's affiliations:

Filippo Santambrogio ¹

¹ CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, place de Lattre de Tassigny, 75775 Paris cedex 16, France

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Filippo Santambrogio. A Modica–Mortola approximation for branched transport. Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 941-945. doi : 10.1016/j.crma.2010.07.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.016/

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