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Constant in two-dimensional $p$-compliance-network problem

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  • 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 a constant $\theta(p)$ appearing usually in $\Gamma$-limit functional of the rescaled $p$-compliance functional.
    Mathematics Subject Classification: Primary: 49J45; Secondary: 49Q10, 74P05.


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