The irrigation problem is the problem of finding an efficient way to transport a measure ${\mu}^{+}$ onto a measure ${\mu}^{-}$. 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.

Keywords: irrigation problem, traffic plans, dynamical cost, stability

@article{COCV_2008__14_4_864_0, author = {Bernot, Marc and Figalli, Alessio}, title = {Synchronized traffic plans and stability of optima}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {864--878}, publisher = {EDP-Sciences}, volume = {14}, number = {4}, year = {2008}, doi = {10.1051/cocv:2008012}, mrnumber = {2451800}, zbl = {1148.49039}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2008012/} }

TY - JOUR AU - Bernot, Marc AU - Figalli, Alessio TI - Synchronized traffic plans and stability of optima JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 SP - 864 EP - 878 VL - 14 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2008012/ DO - 10.1051/cocv:2008012 LA - en ID - COCV_2008__14_4_864_0 ER -

%0 Journal Article %A Bernot, Marc %A Figalli, Alessio %T Synchronized traffic plans and stability of optima %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 864-878 %V 14 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2008012/ %R 10.1051/cocv:2008012 %G en %F COCV_2008__14_4_864_0

Bernot, Marc; Figalli, Alessio. Synchronized traffic plans and stability of optima. ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 4, pp. 864-878. doi : 10.1051/cocv:2008012. http://archive.numdam.org/articles/10.1051/cocv:2008012/

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