Calculus of Variations and Geometric Measure Theory

M. Bonafini - G. Orlandi - E. Oudet

Variational approximation of functionals defined on 1-dimensional connected sets in $\mathbb{R}^n$

created by bonafini on 19 Apr 2019
modified on 20 Jun 2021


Published Paper

Inserted: 19 apr 2019
Last Updated: 20 jun 2021

Journal: Advances in Calculus of Variations
Pages: 17
Year: 2019
Doi: 10.1515/acv-2019-0031


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 $\mathbb{R}^n$. Following the analysis developed for the planar case, we provide a variational approximation through Ginzburg-Landau type energies proving a $\Gamma$-convergence result for $n \geq 3$.

Keywords: $\Gamma$-convergence, Ginzburg-Landau, Gilbert-Steiner problem