Domain perturbations, shift of eigenvalues and capacity

DOI10.1006/jfan.1999.3496zbMath0951.47011OpenAlexW2049361315MaRDI QIDQ1969497

André Noll

Publication date: 11 December 2000

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1999.3496

zbMATH Keywords

capacityLaplace operatordomain perturbationRiemann manifoldspectral boundsHilbert space operators

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Perturbation theory of linear operators (47A55) Eigenvalue problems for linear operators (47A75) General theory of partial differential operators (47F05)

Related Items

Capacity and Faber-Krahn inequality in \(\mathbb R^{n}\), Laplace eigenvalues on regular polygons: a series in \(1/N\), Layer potential techniques in spectral analysis. Part I: Complete asymptotic expansions for eigenvalues of the Laplacian in domains with small inclusions

Cites Work

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• Spectra of manifolds less a small domain
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Potential and scattering theory on wildly perturbed domains
• Scattering length and perturbations of \(-\Delta\) by positive potentials
• Domain perturbations, Brownian motion, capacities, and ground states of Dirichlet Schrödinger operators
• Dirichlet forms and symmetric Markov processes
• Capacitary estimates for Dirichlet eigenvalues
• Approximation of Dirichlet eigenvalues on domains with small holes
• Capacity in abstract hilbert spaces and applications to higher order. differential operators
• On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems
• On linear partial differential equations with analytic coefficients unique continuation of data