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Optimal Shape for Elliptic Problems with Random Perturbations

Buttazzo, Giuseppe and Maestre, Faustino (2010) Optimal Shape for Elliptic Problems with Random Perturbations. arXiv .

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SUMMARY In this paper we analyze the relaxed form of a shape optimization problem with state equation $\{{array}{ll} -div \big(a(x)Du\big)=f\qquad\hbox{in}D \hbox{boundary conditions on}\partial D. {array}.$ The new fact is that the term $f$ is only known up to a random perturbation $\xi(x,\omega)$. The goal is to find an optimal coefficient $a(x)$, fulfilling the usual constraints $\alpha\le a\le\beta$ and $\displaystyle\int_D a(x) dx\le m$, which minimizes a cost function of the form $$\int_\Omega\int_Dj\big(x,\omega,u_a(x,\omega)\big) dx dP(\omega).$$ Some numerical examples are shown in the last section, to stress the difference with respect to the case with no perturbation.

Item Type: Article
Additional Information: Imported from arXiv
Subjects: Area01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica
Divisions: Dipartimenti (from 2013) > DIPARTIMENTO DI MATEMATICA
Depositing User: dott.ssa Sandra Faita
Date Deposited: 05 Aug 2013 12:48
Last Modified: 05 Aug 2013 12:48
URI: http://eprints.adm.unipi.it/id/eprint/1332

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