On an optimal shape design problem in conduction

Bellido, José Carlos

ESAIM: Control, Optimisation and Calculus of Variations, Tome 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.

Classification : 49J45, 49Q10
Mots clés : optimal shape design, relaxation, variational approach, $\Gamma $-convergence, semiconvex envelopes, quasiconvexity

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