[Une approximation à la Modica–Mortola pour le problème de Steiner]
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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@article{CRMATH_2014__352_5_451_0,
author = {Lemenant, Antoine and Santambrogio, Filippo},
title = {A {Modica{\textendash}Mortola} approximation for the {Steiner} {Problem}},
journal = {Comptes Rendus. Math\'ematique},
pages = {451--454},
publisher = {Elsevier},
volume = {352},
number = {5},
year = {2014},
doi = {10.1016/j.crma.2014.03.008},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.03.008/}
}
TY - JOUR AU - Lemenant, Antoine AU - Santambrogio, Filippo TI - A Modica–Mortola approximation for the Steiner Problem JO - Comptes Rendus. Mathématique PY - 2014 SP - 451 EP - 454 VL - 352 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.03.008/ DO - 10.1016/j.crma.2014.03.008 LA - en ID - CRMATH_2014__352_5_451_0 ER -
%0 Journal Article %A Lemenant, Antoine %A Santambrogio, Filippo %T A Modica–Mortola approximation for the Steiner Problem %J Comptes Rendus. Mathématique %D 2014 %P 451-454 %V 352 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.03.008/ %R 10.1016/j.crma.2014.03.008 %G en %F CRMATH_2014__352_5_451_0
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://www.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.
