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Research Article | Open Access

Energy minimizing maps with prescribed singularities and Gilbert-Steiner optimal networks

Sisto Baldo1, Van Phu Cuong Le1, Annalisa Massaccesi2( ), Giandomenico Orlandi1
Dipartimento di Informatica, Università di Verona, Italy
Dipartimento di Tecnica e Gestione dei Sistemi Industriali, Università degli Studi di Padova, Italy
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Abstract

We investigate the relation between energy minimizing maps valued into spheres having topological singularities at given points and optimal networks connecting them (e.g., Steiner trees, Gilbert-Steiner irrigation networks). We show the equivalence of the corresponding variational problems, interpreting in particular the branched optimal transport problem as a homological Plateau problem for rectifiable currents with values in a suitable normed group. This generalizes the pioneering work by Brezis, Coron and Lieb [10].

Keywords

liquid crystalsoptimal mappingsSteiner tree problembranched optimal transporthomological Plateau problemG-currents

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Mathematics in Engineering
Volume 5 Issue 4,
August 2023
Pages 1-19
DOI: 10.3934/mine.2023078

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Cite this article:
Baldo S, Le VPC, Massaccesi A, et al. Energy minimizing maps with prescribed singularities and Gilbert-Steiner optimal networks. Mathematics in Engineering, 2023, 5(4): 1-19. https://doi.org/10.3934/mine.2023078

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Received: 20 October 2022
Revised: 23 February 2023
Accepted: 23 February 2023
Published: 15 August 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)