The spectrum of weighted Laplace operator in unbounded domains
type: Item
instance of: scholarly article
title: The spectrum of weighted Laplace operator in unbounded domains
zbMATH Open document ID: 1233.47042
DOI: 10.1134/S1064562411010169
published in: Doklady Mathematics
publication date: 2012-01-17T00:00:00Z
review text: The author studies the weighted Laplacian \[ Lu=-|x|^s\Delta u,\quad s\geq0 \] over the Hilbert space \(L_{2,s}(\Omega)\) endowed with the norm \(\|u\|^2_{L_{2,s}}=\int_\Omega |x|^{-s}|u|^2\,dx,\) where \(\Omega\subset \mathbb R^n,\) \(n\geq2,\) is an unbounded domain with closure not containing the origin. The dependence of the spectral properties of \(L\) (such as location of the spectrum, its density and structure) on the exponent \(s\) is studied.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 5998329
zbMATH Keywords: weighted Laplace operator
zbMATH Keywords: unbounded domain
zbMATH Keywords: spectrum
author: Alexey Filinovskiy
MaRDI profile type: Publication
cites work: The perturbed Laplace operator in a weighted \(L^ 2\)-space
cites work: Q5526485
cites work: Q5519462
cites work: Q3337807
description: scientific article; zbMATH DE number 5998329