On an optimal shape design problem in conduction
ESAIM: Control, Optimisation and Calculus of Variations, Volume 12 (2006) no. 4, pp. 699-720.

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.

DOI: 10.1051/cocv:2006018
Classification: 49J45, 49Q10
Keywords: optimal shape design, relaxation, variational approach, $\Gamma $-convergence, semiconvex envelopes, quasiconvexity
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     title = {On an optimal shape design problem in conduction},
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Bellido, José Carlos. On an optimal shape design problem in conduction. ESAIM: Control, Optimisation and Calculus of Variations, Volume 12 (2006) no. 4, pp. 699-720. doi : 10.1051/cocv:2006018. http://archive.numdam.org/articles/10.1051/cocv:2006018/

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