An optimal irrigation network with infinitely many branching points

Andrea Marchese and Annalisa Massaccesi

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Submission date: 04. Aug. 2014 (revised version: August 2014)
Pages: 25
published in: Control, optimisation and calculus of variations (ESAIM-COCV), 22 (2016) 2, p. 543-561 
DOI number (of the published article): 10.1051/cocv/2015028
Bibtex
MSC-Numbers: 49Q15, 49Q20, 49N60, 53C38
Keywords and phrases: Gilbert-Steiner problem, irrigation problem, calibrations, flat G-chains
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Abstract:
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, which can be used to prove the optimality of concrete configurations. We apply this technique to prove the optimality of a certain irrigation network, having the topological property mentioned in the title.