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 ℓ2, having countably many branching points and a continuous amount of endpoints.

An optimal irrigation network with infinitely many branching points / Marchese, A.; Massaccesi, A.. - In: ESAIM. COCV. - ISSN 1292-8119. - 2016, 22:2(2016), pp. 543-561. [10.1051/cocv/2015028]

An optimal irrigation network with infinitely many branching points

Marchese A.;Massaccesi A.
2016-01-01

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. We apply this technique to prove the optimality of a certain irrigation network in the separable Hilbert space ℓ2, having countably many branching points and a continuous amount of endpoints.
2016
2
Marchese, A.; Massaccesi, A.
An optimal irrigation network with infinitely many branching points / Marchese, A.; Massaccesi, A.. - In: ESAIM. COCV. - ISSN 1292-8119. - 2016, 22:2(2016), pp. 543-561. [10.1051/cocv/2015028]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/265925
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