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

Al-hassem Nayam; Al-hassem Nayam

doi:10.3934/nhm.2014.9.161

Networks and Heterogeneous Media

2014, Volume 9, Issue 1: 161-168. doi: 10.3934/nhm.2014.9.161

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

Al-hassem Nayam ^{1
,}

1.
International Centre for Theoretical Physics, Strada Costiera,11, I - 34151 Trieste

Received: 01 April 2013 Revised: 01 October 2013
Primary: 49J45; Secondary: 49Q10, 74P05.

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.
- $\Gamma$-convergence,
- shape optimization
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.

References

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