The Gilbert−Steiner problem is a mass transportation problem, where the cost of the transportation depends on the network used to move the mass and it is proportional to a certain power of the “flow”. In this paper, we introduce a new formulation of the problem, which turns it into the minimization of a convex functional in a class of currents with coefficients in a group. This framework allows us to define calibrations. We apply this technique to prove the optimality of a certain irrigation network in the separable Hilbert space , having countably many branching points and a continuous amount of endpoints.
DOI : 10.1051/cocv/2015028
Mots clés : Gilbert−Steiner problem, irrigation problem, calibrations, flatG-chains
@article{COCV_2016__22_2_543_0,
author = {Marchese, Andrea and Massaccesi, Annalisa},
title = {An optimal irrigation network with infinitely many branching points},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {543--561},
publisher = {EDP-Sciences},
volume = {22},
number = {2},
year = {2016},
doi = {10.1051/cocv/2015028},
zbl = {1343.49074},
mrnumber = {3491783},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2015028/}
}
TY - JOUR AU - Marchese, Andrea AU - Massaccesi, Annalisa TI - An optimal irrigation network with infinitely many branching points JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 543 EP - 561 VL - 22 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2015028/ DO - 10.1051/cocv/2015028 LA - en ID - COCV_2016__22_2_543_0 ER -
%0 Journal Article %A Marchese, Andrea %A Massaccesi, Annalisa %T An optimal irrigation network with infinitely many branching points %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 543-561 %V 22 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2015028/ %R 10.1051/cocv/2015028 %G en %F COCV_2016__22_2_543_0
Marchese, Andrea; Massaccesi, Annalisa. An optimal irrigation network with infinitely many branching points. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 2, pp. 543-561. doi : 10.1051/cocv/2015028. http://archive.numdam.org/articles/10.1051/cocv/2015028/
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