Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators

DOI10.1007/s13163-011-0079-2zbMath1302.35271arXiv1012.4961OpenAlexW2083952754MaRDI QIDQ365133

Pier Domenico Lamberti, Victor I. Burenkov

Publication date: 4 September 2013

Published in: Revista Matemática Complutense (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.4961

zbMATH Keywords

elliptic equationsdomain perturbationsharp estimatesDirichlet and Neumann boundary conditionsstability of eigenvalues

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Estimates of eigenvalues in context of PDEs (35P15) Eigenvalue problems for linear operators (47A75) Linear symmetric and selfadjoint operators (unbounded) (47B25)

Related Items (17)

Spectral stability of the Steklov problem ⋮ Conformal spectral stability estimates for the Dirichlet Laplacian ⋮ Convergence of Dirichlet eigenvalues for elliptic systems on perturbed domains ⋮ Spectral stability results for higher-order operators under perturbations of the domain ⋮ Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains ⋮ On the spectral instability for weak intermediate triharmonic problems ⋮ Conformal spectral stability estimates for the Neumann Laplacian ⋮ On the polygonal Faber-Krahn inequality ⋮ Spectral stability of the curlcurl operator via uniform Gaffney inequalities on perturbed electromagnetic cavities ⋮ Spectral stability estimates of Dirichlet divergence form elliptic operators ⋮ Weyl-type bounds for Steklov eigenvalues ⋮ Spectral stability for a class of fourth order Steklov problems under domain perturbations ⋮ Higher order elliptic operators on variable domains. Stability results and boundary oscillations for intermediate problems ⋮ On a Babuška paradox for polyharmonic operators: spectral stability and boundary homogenization for intermediate problems ⋮ Analyticity and Criticality Results for the Eigenvalues of the Biharmonic Operator ⋮ Stability estimates in H01 for solutions of elliptic equations in varying domains ⋮ Shape deformation for vibrating hinged plates

Cites Work

• Spectral stability of general non-negative selfadjoint operators with applications to Neumann-type operators
• Spectral stability of the Neumann Laplacian.
• Spectral stability of Dirichlet second order uniformly elliptic operators
• Spectral Stability of Higher Order Uniformly Elliptic Operators
• On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems
• Stability Estimates for Resolvents, Eigenvalues, and Eigenfunctions of Elliptic Operators on Variable Domains
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