Singular perturbations in shape optimization for the Dirichlet Laplacian

Serguei A. Nazarov; Jan Sokolowski

doi:10.1016/j.crme.2005.02.006

Singular perturbations in shape optimization for the Dirichlet Laplacian

Presented by: Évariste Sanchez-Palencia

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

Comptes Rendus. Mécanique, Volume 333 (2005) no. 4, pp. 305-310.

Abstract
Résumé

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.

Received: 2004-11-30
Accepted: 2005-02-08
Published online: 2005-03-05

DOI: 10.1016/j.crme.2005.02.006

Keywords: Computational solid mechanics, Dirichlet Laplacian, Shape optimization problem
Mots-clés : Mécanique des solides numérique, Laplacien de Dirichlet, Problème d'optimisation de forme

Author's affiliations:

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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     title = {Singular perturbations in shape optimization for the {Dirichlet} {Laplacian}},
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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/

References
Cited by

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[9] M. Bach; S.A. Nazarov Smoothness properties of solutions to variational inequalities describing propagation of mode-1 cracks, Mathematical Aspects of Boundary Element Method (Palaiseau, 1998), CRC Res. Notes Math., vol. 414, Chapman & Hall, London, 2000, pp. 23-32

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