Spectral stability of the Neumann Laplacian.

DOI10.1016/S0022-0396(02)00033-5zbMath1042.35035arXivmath/0106160OpenAlexW2095438542MaRDI QIDQ1867234

Victor I. Burenkov, E. Brian Davies

Publication date: 2 April 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0106160

zbMATH Keywords

Hölder continuitySobolev inequalitiesspectral stabilityHardy inequalitiesNeumann Laplacian

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05) Estimates of eigenvalues in context of PDEs (35P15)

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Cites Work

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• Whitney cubes, p-capacity, and Minkowski content
• The essential spectrum of Neumann Laplacians on some bounded singular domains
• Some embeddings of weighted Sobolev spaces on finite measure and quasibounded domains
• On Neumann's problem in domains with nonregular boundaries
• Compactness of the embedding operators for rough domains
• Fractal Drum, Inverse Spectral Problems for Elliptic Operators and a Partial Resolution of the Weyl-Berry Conjecture
• Weighted Poincaré inequalities and Minkowski content

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