Variational approximation of size-mass energies for k-dimensional currents - Centre de mathématiques appliquées (CMAP) Accéder directement au contenu
Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2019

Variational approximation of size-mass energies for k-dimensional currents

Résumé

In this paper we produce a Γ-convergence result for a class of energies Fε,ak modeled on the Ambrosio-Tortorelli functional. For the choice k = 1 we show that Fε,a1 Γ-converges to a branched transportation energy whose cost per unit length is a function fan−1 depending on a parameter a > 0 and on the codimension n − 1. The limit cost fa(m) is bounded from below by 1 + m so that the limit functional controls the mass and the length of the limit object. In the limit a ↓ 0 we recover the Steiner energy. We then generalize the approach to any dimension and codimension. The limit objects are now k-currents with prescribed boundary, the limit functional controls both their masses and sizes. In the limit a ↓ 0, we recover the Plateau energy defined on k-currents, k < n. The energies Fε,ak then could be used for the numerical treatment of the k-Plateau problem.
Fichier principal
Vignette du fichier
cocv170161.pdf (825.52 Ko) Télécharger le fichier
Origine : Publication financée par une institution
Loading...

Dates et versions

hal-02952640 , version 1 (29-09-2020)

Identifiants

Citer

Antonin Chambolle, Luca A.D. Ferrari, Benoit Merlet. Variational approximation of size-mass energies for k-dimensional currents. ESAIM: Control, Optimisation and Calculus of Variations, 2019, 25, pp.43. ⟨10.1051/cocv/2018027⟩. ⟨hal-02952640⟩
29 Consultations
23 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More