Spectral problems in the shape optimisation. Singular boundary perturbations

Article type: Research Article

Authors: Nazarov, S.A. | Sokolowski, J.

Affiliations: Institute of Mechanical Engineering Problems Russian, Academy of Sciences, Saint-Petersburg, Russia. E-mail: [email protected] | Institut Elie Cartan, Laboratoire de Mathématiques, Université Henri Poincaré Nancy 1, B.P. 239, 54506 Vandoeuvre lès Nancy Cedex, France. E-mail: [email protected]

Abstract: In the paper asymptotic analysis of spectral problems is performed for singular perturbations of geometrical domains. Asymptotic approximations of eigenvalues and eigenfunctions are constructed for the scalar, second-order boundary value problems. The presented results are constructive and can be used in the analysis of shape optimisation and inverse problems.

Keywords: singular perturbations, spectral problem, asymptotics of eigenfunctions and eigenvalues

Journal: Asymptotic Analysis, vol. 56, no. 3-4, pp. 159-204, 2008