Geodesic
Transport Distances and Irrigation Models
Journal of convex analysis, Tome 16 (2009) no. 1, pp. 121-152

Voir la notice de l'article provenant de la source Heldermann Verlag

Some variational models have been recently introduced to the aim of modeling ramified structures, such as trees, rivers and so on. We introduce a general scheme in which the notion of "transport distance" is introduced starting from a general transport cost functional, through relaxation arguments. Then we apply this general framework to the irrigation cost, which is a particular cost functional depending on a parameter α between 0 and 1. We discuss the equivalence between this abstract approach and the above models. 
@article{JCA_2009_16_1_JCA_2009_16_1_a5,
     author = {F. Maddalena and S. Solimini},
     title = {Transport {Distances} and {Irrigation} {Models}},
     journal = {Journal of convex analysis},
     pages = {121--152},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a5/}
}
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F. Maddalena; S. Solimini. Transport Distances and Irrigation Models. Journal of convex analysis, Tome 16 (2009) no. 1, pp. 121-152. http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a5/