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Journal of Convex Analysis 12 (2005), No. 1, 145--158
Copyright Heldermann Verlag 2005

Γ-Convergence for the Irrigation Problem

Sunra J. N. Mosconi
Scuola Normale Superiore, 56126 Pisa, Italy

Paolo Tilli
Scuola Normale Superiore, 56126 Pisa, Italy


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.

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