Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains
From MaRDI portal
Publication:1012360
DOI10.1016/j.anihpc.2007.12.001zbMath1168.35401arXiv0712.3245OpenAlexW2044498902MaRDI QIDQ1012360
Pedro Freitas, Denis I. Borisov
Publication date: 16 April 2009
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0712.3245
Estimates of eigenvalues in context of PDEs (35P15) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)
Related Items (30)
The emergence of eigenvalues of a \(\mathcal{PT}\)-symmetric operator in a thin strip ⋮ Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods ⋮ Discrete spectrum of cranked quantum and elastic waveguides ⋮ The localization for eigenfunctions of the Dirichlet problem in thin polyhedra near the vertices ⋮ Asymptotics of eigenvalues of the Dirichlet problem in a skewed ℐ-shaped waveguide ⋮ Uniform Level Set Estimates for Ground State Eigenfunctions ⋮ Parasitic eigenvalues of spectral problems for the Laplacian with third-type boundary conditions ⋮ Quantum singular operator limits of thin Dirichlet tubes via \(\Gamma\)-convergence ⋮ Eigenvalue asymptotics for almost flat compact hypersurfaces ⋮ Two-dimensional asymptotic models of thin cylindrical elastic gaskets ⋮ Eigenmodes of a thin elastic layer between periodic rigid profiles ⋮ Localization of eigenfunctions in the Dirichlet beaker ⋮ The shape of the level sets of the first eigenfunction of a class of two-dimensional Schrödinger operators ⋮ Localization effects for Dirichlet problems in domains surrounded by thin stiff and heavy bands ⋮ Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals ⋮ On the spectrum and weakly effective operator for Dirichlet Laplacian in thin deformed tubes ⋮ Maximizing Neumann fundamental tones of triangles ⋮ Minimizing Neumann fundamental tones of triangles: an optimal Poincaré inequality ⋮ Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions ⋮ Asymptotics of the eigenvalues of boundary value problems for the Laplace operator in a three-dimensional domain with a thin closed tube ⋮ Asymptotics of the natural oscillations of a thin elastic gasket between absolutely rigid profiles ⋮ Localization effect for Dirichlet eigenfunctions in thin non-smooth domains ⋮ Asymptotic analysis of the high frequencies for the Laplace operator in a thin t-like shaped structure ⋮ Localization of eigenfunctions in a narrow Kirchhoff plate ⋮ Nodal line estimates for the second Dirichlet eigenfunction ⋮ Asymptotics for the expected lifetime of Brownian motion on thin domains in \(\mathbb R^n\) ⋮ On Norm Resolvent and Quadratic Form Convergences in Asymptotic Thin Spatial Waveguides ⋮ Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in \(\mathbb R^d\) ⋮ Planar waveguide with “twisted” boundary conditions: Small width ⋮ Plane waveguides with corners in the small angle limit
Cites Work
- On the spectrum of the Dirichlet Laplacian in a narrow strip
- Precise bounds and asymptotics for the first Dirichlet eigenvalue of triangles and rhombi
- Parameter and domain dependence of eigenvalues of elliptic partial differential equations
- Linear and quasilinear elliptic equations
- A sharp upper bound for the first Dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains
- A numerical study of the spectral gap
- Unnamed Item
- Unnamed Item
This page was built for publication: Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains
