Spectral Stability of the Neumann Laplacian

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We prove the equivalence of Hardy- and Sobolev-type inequalities, certain uniform bounds on the heat kernel and some spectral regularity properties of the Neumann Laplacian associated with an arbitrary region of finite measure in Euclidean space. We also prove that if one perturbs the boundary of the region within a uniform Hölder category then the eigenvalues of the Neumann Laplacian change by a small and explicitly estimated amount. AMS subject classifications: 35P15, 35J25, 47A75, 47B25, 26D10, 46E35. Keywords: Neumann Laplacian, Sobolev inequalities, Hardy inequalities, spectral stability, Hölder continuity.
23 pages

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Spectral Theory, Functional Analysis, 35P15; 35J25, 47A75, 47B25; 26D10; 46E35

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http://salesiana.dossiersoluciones.com/handle/123456789/99000

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0106160
 http://arxiv.org/abs/math/0106160

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arXiv