Journal of Convex Analysis 16 (2009), No. 1, 121--152
Copyright Heldermann Verlag 2009
Transport Distances and Irrigation Models
Francesco Maddalena
Dip. di Matematica, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy
f.maddalena@poliba.it
Sergio Solimini
Dip. di Matematica, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy
solimini@poliba.it
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.
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