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A convex approach to the Gilbert–Steiner problemInterfaces and Free Boundaries
- Publisher
- de Gruyter
- Copyright
- © 2021 Walter de Gruyter GmbH, Berlin/Boston
- ISSN
- 1864-8266
- eISSN
- 1864-8266
- DOI
- 10.1515/acv-2019-0031
- Publisher site
- See Article on Publisher Site
Abstract
AbstractIn 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 ℝn{\mathbb{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, 6, 6307–6332], we provide a variational approximation through Ginzburg–Landau type energies proving a Γ-convergence result for n≥3{n\geq 3}.
Journal
Advances in Calculus of Variations – de Gruyter
Published: Oct 1, 2021
Keywords: Calculus of variations; geometric measure theory; Gamma-convergence; convex relaxation; Gilbert–Steiner problem; 49J45; 49Q20; 49Q15; 49M20; 65K10