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
modified on 04 Nov 2019


Published Paper

Inserted: 7 apr 2019
Last Updated: 4 nov 2019

Journal: Comm. Pure App. Math.
Year: 2019


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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