Comptes Rendus
Singular perturbations in shape optimization for the Dirichlet Laplacian
Comptes Rendus. Mécanique, Volume 333 (2005) no. 4, pp. 305-310.

A shape optimization problem is considered for the Dirichlet Laplacian. Asymptotic analysis is used in order to characterise the optimal shapes which are finally given by a singular perturbation of the smooth initial domain.

Un problème d'optimisation de forme est posé pour l'énergie du Laplacien avec conditions de Dirichlet. Des formes optimales obtenues par l'analyse asymptotique sont données par une perturbation singulière du domain initial régulier.

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Published online:
DOI: 10.1016/j.crme.2005.02.006
Keywords: Computational solid mechanics, Dirichlet Laplacian, Shape optimization problem
Mot clés : Mécanique des solides numérique, Laplacien de Dirichlet, Problème d'optimisation de forme

Serguei A. Nazarov 1; Jan Sokolowski 2

1 Institute of Mechanical Engineering Problems, Laboratory of Mathematical Methods, Russian Academy of Sciences, V.O. Bol'shoi 61, 199178 St. Petersburg, Russia
2 Institut Elie Cartan, laboratoire de mathematiques, université Henri Poincare Nancy I, BP 239, 54506 Vandoeuvre-les-Nancy cedex, France
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Serguei A. Nazarov; Jan Sokolowski. Singular perturbations in shape optimization for the Dirichlet Laplacian. Comptes Rendus. Mécanique, Volume 333 (2005) no. 4, pp. 305-310. doi : 10.1016/j.crme.2005.02.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.02.006/

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