Calculus of Variations and Geometric Measure Theory
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A. Nayam

On some asymptotical shape problems

created by nayam on 21 May 2012
modified on 07 Sep 2013

[BibTeX]

Published Paper

Inserted: 21 may 2012
Last Updated: 7 sep 2013

Journal: J. Asymp. Anal
Volume: 83
Number: 4
Pages: 285-302
Year: 2013

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 a given functional. We look for the optimal region among the class of all closed connected sets of assigned total length $l.$ Then we let $l$ tends to infinity 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.


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