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.
Keywords: 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},
year = {2006},
publisher = {EDP Sciences},
volume = {12},
number = {4},
doi = {10.1051/cocv:2006018},
mrnumber = {2266814},
zbl = {1111.49028},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv:2006018/}
}
TY - JOUR AU - Bellido, José Carlos TI - On an optimal shape design problem in conduction JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2006 SP - 699 EP - 720 VL - 12 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv:2006018/ DO - 10.1051/cocv:2006018 LA - en ID - COCV_2006__12_4_699_0 ER -
%0 Journal Article %A Bellido, José Carlos %T On an optimal shape design problem in conduction %J ESAIM: Control, Optimisation and Calculus of Variations %D 2006 %P 699-720 %V 12 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv:2006018/ %R 10.1051/cocv:2006018 %G en %F COCV_2006__12_4_699_0
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
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