Asymptotics of an optimal compliance-network problem
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Received:
01 October 2012
Revised:
01 March 2013
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Primary: 49J45; Secondary: 49Q10, 74P05.
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We consider the problem of the optimal location of a Dirichlet
region in a $d$-dimensional domain $\Omega$ subjected to a
given force $f$ in order to minimize the $p$-compliance of the
configuration. We look for the optimal region among the class
of all closed connected sets of assigned length $l.$ Then
we let the length $l$ tend to infinity and we look at
the $\Gamma$-limit of a suitable rescaled functional, from which
we get information of the asymptotic distribution of the
optimal region. We also study the case where the Dirichlet
region is a discrete set of finite cardinality.
Citation: Al-hassem Nayam. Asymptotics of an optimal compliance-network problem[J]. Networks and Heterogeneous Media, 2013, 8(2): 573-589. doi: 10.3934/nhm.2013.8.573
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Abstract
We consider the problem of the optimal location of a Dirichlet
region in a $d$-dimensional domain $\Omega$ subjected to a
given force $f$ in order to minimize the $p$-compliance of the
configuration. We look for the optimal region among the class
of all closed connected sets of assigned length $l.$ Then
we let the length $l$ tend to infinity and we look at
the $\Gamma$-limit of a suitable rescaled functional, from which
we get information of the asymptotic distribution of the
optimal region. We also study the case where the Dirichlet
region is a discrete set of finite cardinality.
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