Geodesic
Γ-Convergence for the Irrigation Problem
Journal of convex analysis, Tome 12 (2005) no. 1, pp. 145-158.

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

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. 
@article{JCA_2005_12_1_JCA_2005_12_1_a9,
     author = {S. J. N. Mosconi and P. Tilli},
     title = {\ensuremath{\Gamma}-Convergence for the {Irrigation} {Problem}},
     journal = {Journal of convex analysis},
     pages = {145--158},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2005},
     url = {http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a9/}
}
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S. J. N. Mosconi; P. Tilli. Γ-Convergence for the Irrigation Problem. Journal of convex analysis, Tome 12 (2005) no. 1, pp. 145-158. http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a9/