Abstract

We study the asymptotics of the functional F(γ)=∫f(x)dγ(x)pdxF(\gamma)=\int f(x) d_\gamma(x)^pdx, where dγd_\gamma is the distance function to γ\gamma, among all connected compact sets γ\gamma of given length, when the prescribed length tends to infinity. After properly scaling, we prove the existence of a Γ\Gamma-limit in the space of probability measures, thus retrieving information on the asymptotics of minimal sequences

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Sunra J. N. Mosconi

Scuola Normale Superiore, 56126 Pisa, Italy

mosconi@sns.it

Paolo Tilli

Scuola Normale Superiore, 56126 Pisa, Italy

tilli@sns.it

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Suggested citation

S. J. N. Mosconi, P. Tilli. “Γ-Convergence for the Irrigation Problem.” Journal of Convex Analysis 12 (2005), No. 1, 145–158. https://doi.org/10.68381/jca12010

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Published by Heldermann Verlag, 2005. Rights now held by Banach Press LLC.