Spectral problems in the shape optimisation, singular boundary perturbations

Sergeï A. Nazarov (1) , Jan Sokolowski (2)

1 IPME - Institute of Mechanical Engineering Problems [St. Petersburg]
2 IECN - Institut Élie Cartan de Nancy

In the paper asymptotic analysis of spectral problems is performed for singular pertrurbations 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 optimization and inverse problems.

Mots clés: singular perturbations; spectral problems; asymptotics of eigenfunctions and eigenvalues

Domaines: Equations aux dérivées partielles [math.AP]

Sergeï A. Nazarov, Jan Sokolowski. Spectral problems in the shape optimisation, singular boundary perturbations. 2007. ⟨hal-00174769⟩