Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint
76/2014

An optimal irrigation network with infinitely many branching points

Andrea Marchese and Annalisa Massaccesi

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.

Received:
Aug 4, 2014
Published:
Aug 7, 2014
MSC Codes:
49Q15, 49Q20, 49N60, 53C38
Keywords:
Gilbert-Steiner problem, irrigation problem, calibrations, flat G-chains

Related publications

inJournal
2016 Repository Open Access
Andrea Marchese and Annalisa Massaccesi

An optimal irrigation network with infinitely many branching points

In: Control, optimisation and calculus of variations (ESAIM-COCV), 22 (2016) 2, pp. 543-561