On an optimal shape design problem in conduction
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.

DOI : https://doi.org/10.1051/cocv:2006018
Classification : 49J45,  49Q10
Mots clés : optimal shape design, relaxation, variational approach, $\Gamma$-convergence, semiconvex envelopes, quasiconvexity
@article{COCV_2006__12_4_699_0,
author = {Bellido, Jos\'e Carlos},
title = {On an optimal shape design problem in conduction},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {699--720},
publisher = {EDP-Sciences},
volume = {12},
number = {4},
year = {2006},
doi = {10.1051/cocv:2006018},
zbl = {1111.49028},
mrnumber = {2266814},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2006018/}
}
Bellido, José Carlos. On an optimal shape design problem in conduction. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 4, pp. 699-720. doi : 10.1051/cocv:2006018. http://www.numdam.org/articles/10.1051/cocv:2006018/

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