Spectral stability of the Neumann Laplacian

Burenkov, Victor and Davies, E. B. 2002. Spectral stability of the Neumann Laplacian. Journal of Differential Equations 186 (2) , pp. 485-508. 10.1016/S0022-0396(02)00033-5

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Abstract

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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Neumann Laplacian ; Sobolev inequalities ; Hardy inequalities ; Spectral stability ; Hölder continuity
ISSN:	1090-2732
Last Modified:	04 Jun 2017 01:41
URI:	https://orca.cardiff.ac.uk/id/eprint/1688

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