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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.
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.
Lemenant, Antoine 1 ; Santambrogio, Filippo 2
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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.