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semiconvex envelopes

ESAIM: Control, Optimisation and Calculus of Variations (1)

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On an optimal shape design problem in conduction
José Carlos Bellido
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 12 / Issue 4 / October 2006

Published online by Cambridge University Press:

11 October 2006, pp. 699-720

Print publication:

October 2006
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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.