In this paper, we define a notion of calibration for an approach to the classical Steiner problem in a covering space setting and we give some explicit examples. Moreover, we introduce the notion of calibration in families: the idea is to divide the set of competitors in a suitable way, defining an appropriate (and weaker) notion of calibration. Then, calibrating the candidate minimizers in each family and comparing their perimeter, it is possible to find the minimizers of the minimization problem. Thanks to this procedure we prove the minimality of the Steiner configurations spanning the vertices of a regular hexagon and of a regular pentagon.
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DOI : 10.1051/cocv/2019024
Keywords: Minimal partitions, Steiner problem, covering spaces, calibrations
@article{COCV_2020__26_1_A40_0,
author = {Carioni, Marcello and Pluda, Alessandra},
title = {Calibrations for minimal networks in a covering space setting},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2020},
publisher = {EDP Sciences},
volume = {26},
doi = {10.1051/cocv/2019024},
mrnumber = {4117802},
zbl = {1479.49094},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2019024/}
}
TY - JOUR AU - Carioni, Marcello AU - Pluda, Alessandra TI - Calibrations for minimal networks in a covering space setting JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2019024/ DO - 10.1051/cocv/2019024 LA - en ID - COCV_2020__26_1_A40_0 ER -
%0 Journal Article %A Carioni, Marcello %A Pluda, Alessandra %T Calibrations for minimal networks in a covering space setting %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2019024/ %R 10.1051/cocv/2019024 %G en %F COCV_2020__26_1_A40_0
Carioni, Marcello; Pluda, Alessandra. Calibrations for minimal networks in a covering space setting. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 40. doi: 10.1051/cocv/2019024
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