Capacitary asymptotic expansion of the groundstate to second order

DOI10.1080/03605309808821414zbMath0922.47002OpenAlexW1963923572MaRDI QIDQ4228071

I. McGillivray

Publication date: 1998

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309808821414

zbMATH Keywords

Dirichlet boundary conditionsLaplace-Beltrami operatorcompact Riemannian manifoldweighted capacitynonnegative selfadjoint operatorpotential theoretic conditionsregular irreducible Dirichlet form

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Perturbation theory of linear operators (47A55) Eigenvalue problems for linear operators (47A75) Probabilistic potential theory (60J45)

Related Items (3)

Layer potential techniques in spectral analysis. Part I: Complete asymptotic expansions for eigenvalues of the Laplacian in domains with small inclusions ⋮ Area versus capacity and solidification in the crushed ice model ⋮ Geometric lower bounds for the spectrum of elliptic PDEs with Dirichlet conditions in part

Cites Work

• Estimate on the fundamental frequency of a drum
• Spectra of manifolds less a small domain
• Singular variation of domains and eigenvalues of the Laplacian
• The first eigenvalue of the Laplacian on two dimensional Riemannian manifolds
• Scattering length and perturbations of \(-\Delta\) by positive potentials
• Scattering by obstacles of finite capacity
• Capacitary estimates for Dirichlet eigenvalues
• \(L^ 1\)-properties of intrinsic Schrödinger semigroups
• Singular Hadamard's variation of domains and eigenvalues of the Laplacian. II
• Approximation of Dirichlet eigenvalues on domains with small holes
• Spectrum of manifolds with holes

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