Spectrum of the weighted Laplace operator in unbounded domains

Title:

Spectrum of the weighted Laplace operator in unbounded domains

Creator:

Filinovskiy, Alexey

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:4addd684-ff59-450c-8532-3d321f8a4782
uuid:4addd684-ff59-450c-8532-3d321f8a4782
doi:10.21136/MB.2011.141701

Subject:

Laplace operator, multiplicative perturbation, Dirichlet problem, Friedrichs extension, purely discrete spectra, and purely continuous spectra

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We investigate the spectral properties of the differential operator −r s∆, s ≥ 0 with the Dirichlet boundary condition in unbounded domains whose boundaries satisfy some geometrical condition. Considering this operator as a self-adjoint operator in the space with the norm ||u|| 2 L2,s(Ω) = ∫ Ω r −s |u| 2 dx, we study the structure of the spectrum with respect to the parameter s. Further we give an estimate of the rate of condensation of discrete spectra when it changes to continuous.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

415-427

Source:

Mathematica bohemica | 2011 Volume:136 | Number:4

Harvested from:

CDK

Metadata only:

false