Variational Approximation of Functionals Defined on 1-dimensional Connected Sets: The Planar Case - Université Grenoble Alpes
Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2018

Variational Approximation of Functionals Defined on 1-dimensional Connected Sets: The Planar Case

Résumé

In this paper we consider variational problems involving 1-dimensional connected sets in the Euclidean plane, such as the classical Steiner tree problem and the irrigation (Gilbert-Steiner) problem. We relate them to optimal partition problems and provide a variational approximation through Modica-Mortola type energies proving a full Γ-convergence result. We also introduce a suitable convex relaxation and develop the corresponding numerical implementations. The proposed methods are quite general and the results we obtain can be extended to n-dimensional Euclidean space or to more general manifold ambients, as shown in the companion paper [11].
Fichier principal
Vignette du fichier
steiner_tree.pdf (5.51 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02009439 , version 1 (06-02-2019)

Identifiants

Citer

Mauro Bonafini, Giandomenico Orlandi, Edouard Oudet. Variational Approximation of Functionals Defined on 1-dimensional Connected Sets: The Planar Case. SIAM Journal on Mathematical Analysis, 2018, 50 (6), pp.6307-6332. ⟨10.1137/17M1159452⟩. ⟨hal-02009439⟩
61 Consultations
139 Téléchargements

Altmetric

Partager

More