
Journal of Convex Analysis 12 (2005), No. 1, 145158 Copyright Heldermann Verlag 2005 ΓConvergence for the Irrigation Problem Sunra J. N. Mosconi Scuola Normale Superiore, 56126 Pisa, Italy mosconi@sns.it Paolo Tilli Scuola Normale Superiore, 56126 Pisa, Italy tilli@sns.it [Abstractpdf] We study the asymptotics of the functional $F(\gamma)=\int f(x) d_\gamma(x)^pdx$, where $d_\gamma$ is the distance function to $\gamma$, among all connected compact sets $\gamma$ of given length, when the prescribed length tends to infinity. After properly scaling, we prove the existence of a $\Gamma$limit in the space of probability measures, thus retrieving information on the asymptotics of minimal sequences. [ Fulltextpdf (406 KB)] for subscribers only. 