Spectrum of the weighted Laplace operator in unbounded domains

Filinovskiy, Alexey. "Spectrum of the weighted Laplace operator in unbounded domains." Mathematica Bohemica 136.4 (2011): 415-427. <http://eudml.org/doc/196401>.

@article{Filinovskiy2011,
abstract = {We investigate the spectral properties of the differential operator $-r^s \Delta $, $s\ge 0$ 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 $\Vert u\Vert ^2_\{L_\{2, s\} (\Omega )\}= \int _\{\Omega \} r^\{-s\} |u|^2 \{\rm d\} x $, 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.},
author = {Filinovskiy, Alexey},
journal = {Mathematica Bohemica},
keywords = {Laplace operator; multiplicative perturbation; Dirichlet problem; Friedrichs extension; purely discrete spectra; purely continuous spectra; weighted Laplace operator; Friedrichs extension; purely discrete spectra; purely continuous spectra},
language = {eng},
number = {4},
pages = {415-427},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Spectrum of the weighted Laplace operator in unbounded domains},
url = {http://eudml.org/doc/196401},
volume = {136},
year = {2011},
}

TY - JOUR
AU - Filinovskiy, Alexey
TI - Spectrum of the weighted Laplace operator in unbounded domains
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 4
SP - 415
EP - 427
AB - We investigate the spectral properties of the differential operator $-r^s \Delta $, $s\ge 0$ 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 $\Vert u\Vert ^2_{L_{2, s} (\Omega )}= \int _{\Omega } r^{-s} |u|^2 {\rm d} x $, 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.
LA - eng
KW - Laplace operator; multiplicative perturbation; Dirichlet problem; Friedrichs extension; purely discrete spectra; purely continuous spectra; weighted Laplace operator; Friedrichs extension; purely discrete spectra; purely continuous spectra
UR - http://eudml.org/doc/196401
ER -