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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. [ABSTRACT FROM AUTHOR]

The irrigation problem is the problem of finding an efficient way to transport a measure μ+ onto a measure μ-. By efficient, we mean that a structure that achieves the transport (which, following [Bernot, Caselles and Morel, Publ. Mat. 49 (2005) 417-451], we call traffic plan) is better if it carries the mass in a grouped way rather than in a separate way. This is formalized by considering costs functionals that favorize this property. The aim of this paper is to introduce a dynamical cost functional on traffic plans that we argue to be more realistic. The existence of minimizers is proved in two ways: in some cases, we can deduce it from a classical semicontinuity argument; the other cases are treated by studying the link between our cost and the one introduced in [Bernot, Caselles and Morel, Publ. Mat. 49 (2005) 417-451]. Finally, we discuss the stability of minimizers with respect to specific variations of the cost functional. [ABSTRACT FROM AUTHOR]