Calculus of Variations and Geometric Measure Theory

M. Colombo - A. De Rosa - A. Marchese

On the well-posedness of branched transportation

created by derosa on 07 Apr 2019
modified on 11 Jan 2022


Published Paper

Inserted: 7 apr 2019
Last Updated: 11 jan 2022

Journal: Comm. Pure App. Math.
Year: 2021


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.