Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 17 (2010), No. 2, 583--595Copyright 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 [Abstract-pdf] 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 one-dimensional 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. [ Fulltext-pdf  (131  KB)] for subscribers only.