A domain perturbation problem for elliptic operators

Summary Eigenvalue problems with null boundary data are considered for second order symmetric linear elliptic operators in bounded domains of Euclidean n-space. The main theorems give estimates for the perturbation of the eigenvalues and eigenfunctions under the deformation of attaching an ɛ-handle to the domain. In particular it is proved that the variation of every eigenvalue under such a deformation is of order ϕ(ɛ), where ϕ denotes the reciprocal of the parametrix. Entrata in Redazione il 23 giugno 1976.