We show in full generality the stability of optimal transport paths in branched transport: namely, we prove that any limit of optimal transport 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. © 2020 Wiley Periodicals LLC
On the well-posedness of branched transportation / Colombo, Maria; De Rosa, Antonio; Marchese, Andrea. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 2021, 74:4(2021), pp. 833-864. [10.1002/cpa.21919]
On the well-posedness of branched transportation
Colombo, Maria;Marchese, Andrea
2021-01-01
Abstract
We show in full generality the stability of optimal transport paths in branched transport: namely, we prove that any limit of optimal transport 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. © 2020 Wiley Periodicals LLC| File | Dimensione | Formato | |
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Comm Pure Appl Math - 2020 - Colombo - On the Well‐Posedness of Branched Transportation.pdf
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