Variational approximation of functionals defined on 1-dimensional connected sets in ℝn
Keyword(s):
AbstractIn 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 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\geq 3}.
2019 ◽
Vol 25
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pp. 43
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2018 ◽
Vol 50
(6)
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pp. 6307-6332
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2006 ◽
Vol 27
(6)
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pp. 615-636
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2001 ◽
Vol 353
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pp. 4173-4187
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2008 ◽
Vol 16
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pp. 148-175
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