Variational approximation of functionals defined on $1$-dimensional connected sets in $\mathbb{R}^n$
Year: 2019
Type: preprint
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 $Γ$-convergence result for $n \geq 3$.
Source: arXiv (Cornell University)
Institutions: University of Trento, University of Verona
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2936735358