Calculus of Variations and Geometric Measure Theory
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M. Carioni - A. Marchese - A. Massaccesi - A. Pluda - R. Tione

The oriented mailing problem and its convex relaxation

created by marchese on 25 Feb 2019
modified by pluda on 12 Jan 2021

[BibTeX]

Published Paper

Inserted: 25 feb 2019
Last Updated: 12 jan 2021

Journal: Nonlinear Anal.
Volume: 199
Year: 2020
Doi: 10.1016/j.na.2020.112035

Abstract:

In this note we introduce a new model for the mailing problem in branched transportation that takes into account the orientation of the moving particles. This gives an effective answer to Problem 15.9 of the book Optimal transportation Networks, by Bernot, Caselles, and Morel. Moreover we define a convex relaxation in terms of rectifiable currents with group coefficients. We provide the problem with a notion of calibration. Using similar techniques we define a convex relaxation and a corresponding notion of calibration for a variant of the Steiner tree problem in which a connectedness constraint is assigned only among a certain partition of a given set of finitely many points.


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