On the Well‐Posedness of Branched Transportation

On the Well‐Posedness of Branched Transportation

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...

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Veröffentlicht in:Communications on pure and applied mathematics 2021-04, Vol.74 (4), p.833-864
Hauptverfasser: Colombo, Maria, De Rosa, Antonio, Marchese, Andrea
Format: Artikel
Sprache:eng
Schlagworte:
Transportation networks
Well posed problems
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Zusammenfassung: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
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21919