Spectral problems in the shape optimisation. Singular boundary perturbations
С. А. Назаров, Jan Sokołowski · Asymptotic Analysis · 2008
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.