Spectral stability results for higher-order operators under perturbations of the domain |
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Authors: | José M. Arrieta Pier Domenico Lamberti |
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Affiliation: | 1. Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain;2. Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy |
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Abstract: | We analyze the spectral behavior of higher-order elliptic operators when the domain is perturbed. We provide general spectral stability results for Dirichlet and Neumann boundary conditions. Moreover, we study the bi-harmonic operator with the so-called intermediate boundary conditions. We give special attention to this last case and analyze its behavior when the boundary of the domain has some oscillatory behavior. We will show that there is a critical oscillatory behavior and that the limit problem depends on whether we are above, below or just sitting on this critical value. |
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