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Comptes Rendus Mathématique
Volume 348, n° 15-16
pages 941-945 (août 2010)
Doi : 10.1016/j.crma.2010.07.016
Received : 14 June 2010 ;  accepted : 16 July 2010
A Modica–Mortola approximation for branched transport
Une approximation à la Modica–Mortola pour le transport branché
 

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

Abstract

The   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.

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Résumé

L'énergie   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.

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