| Abstract: |
| We consider eigenproblems for elliptic operators in bounded domains, namely the Dirichlet Laplacian. Suppose to perturb the problem in one of the following ways: removing a small hole from the interior of the domain, attaching a thin tube at a boundary point, disrupting the Dirichlet boundary condition with a Neumann condition in a small part of the boundary. In all these cases the operator`s spectrum is stable and eigenvalues can be continued as the perturbation parameter tends to zero. We can prove the sharp asymptotic behavior of eigenbranches which will strongly rely on the local behavior of the limit eigenfunctions at the perturbation point. |
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