On a phase field approximation of the planar Steiner problem: existence, regularity, and asymptotic of minimizers
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Publication:1650258
DOI10.4171/IFB/397zbMath1396.49027arXiv1611.07875OpenAlexW2962898123MaRDI QIDQ1650258
Matthieu Bonnivard, Vincent Millot, Antoine Lemenant
Publication date: 2 July 2018
Published in: Interfaces and Free Boundaries (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1611.07875
Steiner problemGinzburg-Landau functional\(\Gamma\)-convergencephase field approximationaverage distanceoptimal complianceModica-Mortola
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Connected perimeter of planar sets ⋮ Convex relaxation and variational approximation of the Steiner problem: theory and numerics ⋮ Variational Approximation of Functionals Defined on 1-dimensional Connected Sets: The Planar Case ⋮ A finer singular limit of a single-well Modica-Mortola functional and its applications to the Kobayashi-Warren-Carter energy ⋮ Convex relaxation and variational approximation of functionals defined on 1-dimensional connected sets ⋮ Variational approximation of functionals defined on \(1\)-dimensional connected sets in \(\mathbb{R}^n\) ⋮ Numerical approximation of the Steiner problem in dimension $2$ and $3$
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