# American Institute of Mathematical Sciences

doi: 10.3934/dcds.2021167
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## Stability of optimal traffic plans in the irrigation problem

 1 EPFL SB, Station 8, CH-1015 Lausanne, Switzerland 2 Department of Mathematics, University of Maryland, 4176 Campus Dr, College Park, MD 20742, USA 3 Department of Decision Sciences and BIDSA, Bocconi University, Via Röntgen 1, 20136 Milano MI Italy 4 Dipartimento di Matematica, University of Trento, Via Sommarive, 14, 38123 Povo, Italy 5 CEREMADE, CNRS, UMR 7534, Université Paris-Dauphine, PSL University, INRIA Paris, Project team Mokaplan, 75016 Paris, France 6 DER de Mathématiques, ENS Paris-Saclay, Université Paris-Saclay, 91190 Gif-sur-Yvette, France

* Corresponding author: Antonio De Rosa

Received  May 2021 Revised  August 2021 Early access November 2021

Fund Project: The first author is partially supported by the Swiss National Science Foundation grant 200021_182565. The second author is partially supported by the NSF DMS Grant No. 1906451 and the NSF DMS Grant No. 2112311. The third author is partially supported by GNAMPA-INdAM

We prove the stability of optimal traffic plans in branched transport. In particular, we show that any limit of optimal traffic plans is optimal as well. This result goes beyond the Eulerian stability proved in [7], extending it to the Lagrangian framework.

Citation: Maria Colombo, Antonio De Rosa, Andrea Marchese, Paul Pegon, Antoine Prouff. Stability of optimal traffic plans in the irrigation problem. Discrete & Continuous Dynamical Systems, doi: 10.3934/dcds.2021167
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##### References:
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