*Published Paper*

**Inserted:** 26 apr 2013

**Last Updated:** 1 may 2016

**Journal:** Network and heterogeneous media

**Year:** 2013

**Abstract:**

We consider the problem of the minimization of the $p$-compliance functional where the control variables $\Sigma$ are taking among closed connected one-dimensional sets. we prove some estimate from below of the $p$-compliance functional in terms of the one-dimensional Hausdorff measure of $\Sigma$ and compute the value of the constant $\theta(p)$ appearing usually in $\Gamma$-limit functional of the rescaled p-compliance functional.

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