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On an optimal shape design problem in conduction

Published online by Cambridge University Press:  11 October 2006

José Carlos Bellido
José Carlos Bellido*
Affiliation:
Mathematical Institute, University of Oxford, 24-29 St. Giles', OX1 3LB, Oxford, UK; JoseCarlos.Bellido@uclm.es (On leave from Universidad de Castilla-La Mancha (Spain).)
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Abstract

In this paper we analyze a typical shape optimization problem intwo-dimensional conductivity. We study relaxation for this problemitself. We also analyze the question of the approximation of thisproblem by the two-phase optimal design problems obtained when wefill out the holes that we want to design in the original problemby a very poor conductor, that we make to converge to zero.

Keywords

Optimal shape designrelaxationvariational approachΓ-convergencesemiconvex envelopesquasiconvexity.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 4 , October 2006 , pp. 699 - 720
Copyright
© EDP Sciences, SMAI, 2006

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