Home Mathematics Variational approximation of functionals defined on 1-dimensional connected sets in ℝ n
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Variational approximation of functionals defined on 1-dimensional connected sets in ℝ n

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Published/Copyright: February 18, 2020

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 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 .


Communicated by Frank Duzaar


Award Identifier / Grant number: LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01)

Award Identifier / Grant number: project COMEDIC

Funding statement: The first and second author are partially supported by GNAMPA-INdAM. The third author gratefully acknowledges the support of the ANR through the project GEOMETRYA, the project COMEDIC and the LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01).

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Received: 2019-04-18
Accepted: 2020-01-28
Published Online: 2020-02-18
Published in Print: 2021-10-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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