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

## Abstract

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 |
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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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