
Journal of Convex Analysis 17 (2010), No. 2, 583595 Copyright Heldermann Verlag 2010 Some Explicit Examples of Minimizers for the Irrigation Problem Paolo Tilli Dip. di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy paolo.tilli@polito.it [Abstractpdf] We construct some examples of explicit solutions to the problem \[ \min_\gamma \int_\Omega d_\gamma(x)\,dx \] where the minimum is over all connected compact sets $\gamma\subset \overline\Omega\subset{\mathbb R}^2$ of prescribed onedimensional Hausdorff measure. More precisely we show that, if $\gamma$ is a $C^{1,1}$ curve of length $l$ with curvature bounded by $1/R$, $l \leq\pi R$ and $\varepsilon\leq R$, then $\gamma$ is a solution to the above problem with $\Omega$ being the $\varepsilon$neighbourhood of $\gamma$. In particular, $C^{1,1}$ regularity is optimal for this problem. [ Fulltextpdf (131 KB)] for subscribers only. 