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

2019/04/19 by Mauro Bonafini, Bonafini, Mauro, Giandomenico Orlandi +3
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Computational Geometry and Mesh Generation #FOS: Mathematics #Optimization and Control (math.OC) #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.1904.09328

openalex publication_date 2019/04/19 · openalex created_date 2019/04/25 · openalex updated_date 2026/07/28

Abstract

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 ℝⁿ. Following the the analysis for the planar case presented in [4], we provide a variational approximation through Ginzburg--Landau type energies proving a Γ-convergence result for n ≥ 3.

Citations

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

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