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

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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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     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},
     mrnumber = {2266814},
     zbl = {1111.49028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006018/}
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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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