On the spectrum of the Dirichlet Laplacian for Horn-shaped regions in \(R^ n\) with infinite volume

DOI10.1016/0022-1236(84)90036-3zbMath0559.35057OpenAlexW2058529503MaRDI QIDQ2266173

Michiel van den Berg

Publication date: 1984

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(84)90036-3

zbMATH Keywords

traceDirichlet Laplaciandistribution of the eigenvalueshorn-shaped region

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Asymptotic distributions of eigenvalues in context of PDEs (35P20)

Related Items (18)

On the asymptotics of the heat equation and bounds on traces associated with the Dirichlet Laplacian ⋮ Optimization Problems Involving the First Dirichlet Eigenvalue and the Torsional Rigidity ⋮ Heat flow out of regions in \({\mathbb{R}}^ m\) ⋮ Refined asymptotic expansion for the partition function of unbounded quantum billiards ⋮ Spectral estimates for the Dirichlet Laplacian on spiral-shaped regions ⋮ Non-classical spectral bounds for Schrödinger operators ⋮ Intrinsic ultracontractivity and ground state estimates of non-local Dirichlet forms on unbounded open sets ⋮ Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps ⋮ Dirichlet-Neumann bracketing for horn-shaped regions ⋮ Spectral properties of Neumann Laplacian of horns ⋮ The Trace of the Heat Kernel in Lipschitz Domains ⋮ On the spectral counting function for the Dirichlet Laplacian ⋮ Spectral asymptotics with a remainder estimate of the Neumann Laplacian on horns: the case of the rapidly growing counting function ⋮ SHARP SPECTRAL ESTIMATES IN DOMAINS OF INFINITE VOLUME ⋮ Unnamed Item ⋮ Spectral asymptotics of Laplacians on horns: The case of a rapidly growing counting function ⋮ Trace properties of the Dirichlet Laplacian ⋮ The eigenvalue distribution of degenerate Dirichlet forms

Cites Work

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• Nonclassical eigenvalue asymptotics
• Some quantum operators with discrete spectrum but classically continuous spectrum
• Trace properties of the Dirichlet Laplacian
• Comportement asymptotique des valeurs propres d'opérateurs du type Schrödinger à potentiel dégénérée
• Bounds on Green’s functions of second-order differential equations
• The asymptotic distribution of eigenvalues of the Laplace operator in an unbounded domain
• Can One Hear the Shape of a Drum?
• ON THE EIGENVALUES OF THE FIRST BOUNDARY VALUE PROBLEM IN UNBOUNDED DOMAINS
• On Spectra of Second-Order Differential Operators

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