Constant in two-dimensional $p$-compliance-network problem
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Received:
01 April 2013
Revised:
01 October 2013
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Primary: 49J45; Secondary: 49Q10, 74P05.
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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.
Citation: Al-hassem Nayam. Constant in two-dimensional $p$-compliance-network problem[J]. Networks and Heterogeneous Media, 2014, 9(1): 161-168. doi: 10.3934/nhm.2014.9.161
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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 a constant
$\theta(p)$ appearing usually in $\Gamma$-limit functional of the rescaled $p$-compliance
functional.
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