Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain

zbMath1253.47031arXiv1105.5182MaRDI QIDQ2884720

Rupert L. Frank, Leander Geisinger

Publication date: 18 May 2012

Full work available at URL: https://arxiv.org/abs/1105.5182

zbMATH Keywords

eigenvaluesspectral asymptoticssemiclassical limitWeyl's lawDirichlet Laplace operator

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) General theory of partial differential operators (47F05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (12)

Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain ⋮ Bounds for eigenvalues of the Dirichlet problem for the logarithmic Laplacian ⋮ Semiclassical estimates for eigenvalue means of Laplacians on spheres ⋮ On the remainder term of the Berezin inequality on a convex domain ⋮ Semi-classical analysis of the Laplace operator with Robin boundary conditions ⋮ Spectral properties of the Dirichlet operator $\sum _{i=1}^{d}(-\partial _i^2)^{s}$∑i=1d(−∂i2)s on domains in d-dimensional Euclidean space ⋮ A short proof of Weyl's law for fractional differential operators ⋮ Semiclassical bounds for spectra of biharmonic operators ⋮ Semiclassical asymptotics for a class of singular Schrödinger operators ⋮ Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains ⋮ The partition function of the Dirichlet operator \(\mathcal{D}_{2 s} = \sum_{i = 1}^d(-\partial_i^2)^s\) on a \(d\)-dimensional rectangle cavity ⋮ On the spectral asymptotics for the buckling problem

This page was built for publication: Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain