Calculus of Variations and Geometric Measure Theory
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A. Nayam

Asymptotics of an optimal compliance-network problem

created by nayam on 22 May 2012
modified on 07 Sep 2013

[BibTeX]

Published Paper

Inserted: 22 may 2012
Last Updated: 7 sep 2013

Journal: Netw. Herog. Media
Volume: 8
Number: 2
Pages: 573-589
Year: 2013

Abstract:

We consider the problem of the optimal location of a Dirichlet region in a $d$-dimensional domain subjected to a given force $f$ in order to minimize the $p$-compliance of the con guration. We look for the optimal region among the class of all closed connected sets of assigned length $l$: Then we let $l$ tends to in nity and we look at the $\Gamma$-limit of a suitable rescaled functional, in order to get information of the asymptotic distribution of the optimal region. We highlight as well the case where the Dirichlet region is searched among discrete sets of nite cardinality.


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