On the Eigenvalues of the Laplace Operator on a Thin Set with Neumann Boundary Conditions

DOI10.1080/00036819608840461zbMath0865.35098OpenAlexW1968153219WikidataQ58131812 ScholiaQ58131812MaRDI QIDQ4888877

Michelle Schatzman

Publication date: 5 June 1997

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036819608840461

zbMATH Keywords

eigenvalueLaplace-Beltrami operatorNeumann problemthin set

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (16)

Spectral Properties of High Contrast Band-Gap Materials and Operators on Graphs ⋮ THE EFFECTIVE HAMILTONIAN IN CURVED QUANTUM WAVEGUIDES UNDER MILD REGULARITY ASSUMPTIONS ⋮ Influence of bounded states in the Neumann Laplacian in a thin waveguide ⋮ Asymptotics for thin superconducting rings ⋮ On the spectral instability for weak intermediate triharmonic problems ⋮ On the eigenvalues of the biharmonic operator with Neumann boundary conditions on a thin set ⋮ Error estimate for classical solutions to the heat equation in a moving thin domain and its limit equation ⋮ Location of hot spots in thin curved strips ⋮ Navier-Stokes equations in a curved thin domain. II: Global existence of a strong solution ⋮ Effective Hamiltonians in surfaces of thin quantum waveguides ⋮ Convergence of spectra of mesoscopic systems collapsing onto a graph ⋮ Average of the Navier's law on the rapidly oscillating boundary ⋮ Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions ⋮ Navier-Stokes equations in a curved thin domain. III: Thin-film limit ⋮ Asymptotic behavior for the principal eigenvalue of a reinforcement problem ⋮ Krein formula with compensated singularities for the ND-mapping and the generalized Kirchhoff condition at the Neumann Schrödinger junction

Cites Work

• Elliptic Partial Differential Equations of Second Order
• Unnamed Item

This page was built for publication: On the Eigenvalues of the Laplace Operator on a Thin Set with Neumann Boundary Conditions