  We prove estimates for the variation of the eigenvalues of uniformly elliptic
operators with homogeneous Dirichlet or Neumann boundary conditions upon
variation of the open set on which an operator is defined. We consider
operators of arbitrary even order and open sets admitting arbitrary strong
degeneration. The main estimate is expressed via a natural and easily
computable distance between open sets with continuous boundaries. Another
estimate is obtained via the lower Hausdorff-Pompeiu deviation of the
boundaries, which in general may be much smaller than the usual
Hausdorff-Pompeiu distance. Finally, in the case of diffeomorphic open sets we
obtain an estimate even without the assumption of continuity of the boundaries.
