Asymptotic eigenvalue estimates for a Robin problem with a large parameter

DOI10.4171/PM/1945zbMath1295.35346arXiv1312.7293MaRDI QIDQ399392

Leonid Parnovski, Pavel Exner, Alexander A. Minakov

Publication date: 19 August 2014

Published in: Portugaliae Mathematica. Nova Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.7293

zbMATH Keywords

LaplacianRobin problemasymptotic eigenvalue estimates

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (24)

On the isoperimetric inequality for the magnetic Robin Laplacian with negative boundary parameter ⋮ An effective Hamiltonian for the eigenvalue asymptotics of the Robin Laplacian with a large parameter ⋮ Tunneling for the Robin Laplacian in smooth planar domains ⋮ Curvature-induced bound states in Robin waveguides and their asymptotical properties ⋮ Singular Schrödinger operators and Robin billiards. Spectral properties and asymptotic expansions ⋮ Magnetic perturbations of the Robin Laplacian in the strong coupling limit ⋮ Parasitic eigenvalues of spectral problems for the Laplacian with third-type boundary conditions ⋮ Eigenvalues for the Robin Laplacian in domains with variable curvature ⋮ Asymptotics of Robin eigenvalues for non-isotropic peaks ⋮ On the Discrete Spectrum of Robin Laplacians in Conical Domains ⋮ Spectral asymptotics for Robin Laplacians on polygonal domains ⋮ Sum of the negative eigenvalues for the semi-classical Robin Laplacian ⋮ Localization effects for Dirichlet problems in domains surrounded by thin stiff and heavy bands ⋮ Tunneling between corners for Robin Laplacians ⋮ Weyl formulae for the Robin Laplacian in the semiclassical limit ⋮ On the eigenvalues of quantum graph Laplacians with large complex \(\delta\) couplings ⋮ Effective operators for Robin eigenvalues in domains with corners ⋮ Generalized interactions supported on hypersurfaces ⋮ Mean curvature bounds and eigenvalues of Robin Laplacians ⋮ Diamagnetism versus Robin condition and concentration of ground states ⋮ On the eigenvalues of the Robin Laplacian with a complex parameter ⋮ ON THE ASYMPTOTIC BEHAVIOR OF EIGENVALUES AND EIGENFUNCTIONS OF THE ROBIN PROBLEM WITH LARGE PARAMETER ⋮ The first Robin eigenvalue with negative boundary parameter ⋮ The Bilaplacian with Robin Boundary Conditions

Cites Work

• On the asymptotic behaviour of the eigenvalues of a Robin problem.
• Asymptotics of eigenvalues of the Schrödinger operator with a strong \(\delta\)-interaction on a loop
• Bound states in curved quantum waveguides
• Leaky Quantum Graphs: A Review

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