Capacity and Faber-Krahn inequality in \(\mathbb R^{n}\)

DOI10.1016/j.jfa.2005.04.015zbMath1100.31005OpenAlexW1996869359MaRDI QIDQ2368783

Bruno Colbois, Jérôme Bertrand

Publication date: 28 April 2006

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2005.04.015

zbMATH Keywords

capacityeigenvalue estimatesDirichlet spectrumcompact Riemannian manifold with boundaryconvergence of the spectrum

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Potentials and capacities on other spaces (31C15)

Related Items (8)

Uniform stability of the Dirichlet spectrum for rough outer perturbations ⋮ Spectral stability under removal of small capacity sets and applications to Aharonov-Bohm operators ⋮ A sharp upper bound for the first Dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains ⋮ Perturbed eigenvalues of polyharmonic operators in domains with small holes ⋮ The spectrum of the Laplacian: A geometric approach ⋮ On simple eigenvalues of the fractional Laplacian under removal of small fractional capacity sets ⋮ Wildly perturbed manifolds: norm resolvent and spectral convergence ⋮ Ramification of multiple eigenvalues for the Dirichlet-Laplacian in perforated domains

Cites Work

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• The stability of some eigenvalue estimates
• Potential and scattering theory on wildly perturbed domains
• Confinement of Brownian motion among Poissonian obstacles in \(\mathbb{R}^d, d\geq 3\)
• Fluctuations of principal eigenvalues and random scales
• Capacitary estimates for Dirichlet eigenvalues
• Dirichlet problems on varying domains.
• Approximation of Dirichlet eigenvalues on domains with small holes
• Spectrum of manifolds with holes
• Domain perturbations, shift of eigenvalues and capacity
• A quantitative isoperimetric inequality in n-dimensional space.

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