Geodesic
An optimal irrigation network with infinitely many branching points
Marchese, Andrea1 ; Massaccesi, Annalisa2
1 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22, 04103 Leipzig, Germany
2 Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 2, pp. 543-561

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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 ℓ 2 , having countably many branching points and a continuous amount of endpoints.

Reçu le :
DOI : 10.1051/cocv/2015028
Classification : 49Q15, 49Q20, 49N60, 53C38
Keywords: Gilbert−Steiner problem, irrigation problem, calibrations, flatG-chains

Marchese, Andrea 1 ; Massaccesi, Annalisa 2

1 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22, 04103 Leipzig, Germany
2 Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland 
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     title = {An optimal irrigation network with infinitely many branching points},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {543--561},
     publisher = {EDP-Sciences},
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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

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