Published Paper

Inserted: 23 dec 2021
Last Updated: 16 mar 2023

Journal: Mathematics in Engineering
Volume: 5
Year: 2023
Doi: 10.3934/mine.2023078

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: Irrigation problem, Steiner problem, Plateau problem, Calibration, Harmonic maps

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