Viewing the Steklov Eigenvalues of the Laplace Operator as Critical Neumann Eigenvalues

DOI10.1007/978-3-319-12577-0_21zbMath1325.35124arXiv1410.0517OpenAlexW2169938562MaRDI QIDQ2949270

Luigi Provenzano, Pier Domenico Lamberti

Publication date: 8 October 2015

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.0517

zbMATH Keywords

optimizationeigenvaluesLaplace operatorSteklov boundary conditions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (18)

On Vibrating Thin Membranes with Mass Concentrated Near the Boundary: An Asymptotic Analysis ⋮ Scaling inequalities for spherical and hyperbolic eigenvalues ⋮ A comparison between Neumann and Steklov eigenvalues ⋮ On an Interior Calderón Operator and a Related Steklov Eigenproblem for Maxwell's Equations ⋮ Optimal configuration and symmetry breaking phenomena in the composite membrane problem with fractional Laplacian ⋮ From Steklov to Neumann via homogenisation ⋮ Weyl-type bounds for Steklov eigenvalues ⋮ Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems ⋮ A note on Kuttler-Sigillito's inequalities ⋮ Eigenvalues of elliptic operators with density ⋮ Steklov eigenvalues and quasiconformal maps of simply connected planar domains ⋮ Steklov and Robin isospectral manifolds ⋮ Large Steklov eigenvalues via homogenisation on manifolds ⋮ Optimizing information transmission rates drives brain gyrification ⋮ Computation of free boundary minimal surfaces via extremal Steklov eigenvalue problems ⋮ A few shape optimization results for a biharmonic Steklov problem ⋮ On the spectra of three Steklov eigenvalue problems on warped product manifolds ⋮ On the first Steklov-Dirichlet eigenvalue for eccentric annuli

Cites Work

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• Critical points of the symmetric functions of the eigenvalues of the Laplace operator and overdetermined problems
• Absence of critical mass densities for a vibrating membrane
• Flux terms and Robin boundary conditions as limit of reactions and potentials concentrating at the boundary
• On the first positive Neumann eigenvalue
• On the sharpness of a certain spectral stability estimate for the Dirichlet Laplacian
• A maximum principle in spectral optimization problems for elliptic operators subject to mass density perturbations

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