Calculus of variations
A Modica–Mortola approximation for the Steiner Problem
[Une approximation à la Modica–Mortola pour le problème de Steiner]
Comptes Rendus. Mathématique, Tome 352 (2014) no. 5, pp. 451-454.

Dans cette note, nous présentons une méthode d'approximation du problème de Steiner par une famille de fonctionnelles de type Modica–Mortola, avec un terme additionnel basé sur une distance géodésique à poids, pour prendre en compte la contrainte de connexité.

In this note we present a way to approximate the Steiner Problem by a family of elliptic energies of Modica–Mortola type, with an additional term relying on a weighted geodesic distance which takes care of the connectedness constraint.

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DOI : 10.1016/j.crma.2014.03.008
Lemenant, Antoine 1 ; Santambrogio, Filippo 2

1 Université Paris-Diderot, Laboratoire Jacques-Louis-Lions, France
2 Université Paris-Sud, Laboratoire de mathématiques d'Orsay, France
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Lemenant, Antoine; Santambrogio, Filippo. A Modica–Mortola approximation for the Steiner Problem. Comptes Rendus. Mathématique, Tome 352 (2014) no. 5, pp. 451-454. doi : 10.1016/j.crma.2014.03.008. http://archive.numdam.org/articles/10.1016/j.crma.2014.03.008/

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This work has been partially supported by the Agence Nationale de la Recherche, through the project ANR-12-BS01-0014-01 GEOMETRYA, and by The Gaspard Monge Program for Optimization and operations research (PGMO) via the project MACRO.