The irrigation problem is the problem of finding an efficient way to transport a measure onto a measure . 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},
year = {2008},
publisher = {EDP Sciences},
volume = {14},
number = {4},
doi = {10.1051/cocv:2008012},
mrnumber = {2451800},
zbl = {1148.49039},
language = {en},
url = {https://www.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 - https://www.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 https://www.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, Tome 14 (2008) no. 4, pp. 864-878. doi: 10.1051/cocv:2008012
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