Variational approximation of functionals defined on 1-dimensional connected sets in Rn

被引：3

作者：

Bonafini, Mauro ^{[1
]}

Orlandi, Giandomenico ^{[2
]}

Oudet, Edouard ^{[3
]}

机构：

[1] Tech Univ Munich, Fak Math, Garching, Germany

[2] Univ Verona, Dipartimento Informat, Verona, Italy

[3] Univ Grenoble Alpes, Lab Jean Kuntzmann, Grenoble, France

来源：

ADVANCES IN CALCULUS OF VARIATIONS | 2021年 / 14卷 / 04期

关键词：

Calculus of variations; geometric measure theory; Gamma-convergence; convex relaxation; Gilbert-Steiner problem; PHASE-FIELD APPROXIMATION; STEINER PROBLEM;

D O I：

10.1515/acv-2019-0031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the Euclidean Steiner tree problem and, more generally, (single sink) Gilbert-Steiner problems as prototypical examples of variational problems involving 1-dimensional connected sets in R-n. Following the analysis for the planar case presented in [M. Bonafini, G. Orlandi and E. Oudet, Variational approximation of functionals defined on 1-dimensional connected sets: The planar case, SIAM J. Math. Anal. 50 (2018), no. 6, 6307-6332], we provide a variational approximation through Ginzburg-Landau type energies proving a Gamma-convergence result for n >= 3.

引用

页码：541 / 553

页数：13

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