1. Spectrum of the weighted Laplace operator in unbounded domains
- Creator:
- Filinovskiy, Alexey
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Laplace operator, multiplicative perturbation, Dirichlet problem, Friedrichs extension, purely discrete spectra, and purely continuous spectra
- Language:
- English
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public