Calculus of Variations and Geometric Measure Theory
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M. Colombo - A. De Rosa - A. Marchese

On the well-posedness of branched transportation

created by derosa on 07 Apr 2019

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Submitted Paper

Inserted: 7 apr 2019
Last Updated: 7 apr 2019

Year: 2019

Abstract:

We show in full generality the stability of optimal traffic paths in branched transport: namely we prove that any limit of optimal traffic paths is optimal as well. This solves an open problem in the field (cf. Open problem 1 in the book Optimal transportation networks, by Bernot, Caselles and Morel), which has been addressed up to now only under restrictive assumptions.


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