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 on 26 Feb 2019

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Submitted Paper

Inserted: 25 feb 2019
Last Updated: 26 feb 2019

Year: 2019

Abstract:

In this note we introduce a new model for the mailing problem in branched transportation in order to allow the cost functional to take 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. With such approach 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 poi


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