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arXiv · 1904.09328

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

Mauro Bonafini·Giandomenico Orlandi·Edouard Oudet
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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 $\mathbb{R}^n$. Following the the analysis for the planar case presented in [4], we provide a variational approximation through Ginzburg--Landau type energies proving a $\Gamma$-convergence result for $n \geq 3$.

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Mauro Bonafini, Giandomenico Orlandi, Edouard Oudet. 2019-04-19. Variational approximation of functionals defined on $1$-dimensional connected sets in $\mathbb{R}^n$. https://arxiv.org/abs/1904.09328

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