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Issue ESAIM: COCV
Volume 12, Number 4, October 2006
Page(s) 699 - 720
DOI 10.1051/cocv:2006018
Published online 11 October 2006

ESAIM: COCV, October 2006, Vol. 12, pp. 699-720
DOI: 10.1051/cocv:2006018

On an optimal shape design problem in conduction

José Carlos Bellido

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).)


(Received May 13, 2005. Published online 11 October 2006.)

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


Mathematics Subject Classification. 49J45, 49Q10.

Key words: Optimal shape design, relaxation, variational approach, $\Gamma$-convergence, semiconvex envelopes, quasiconvexity.


© EDP Sciences, SMAI 2006


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