Filinovskiy Alexey, Department of High Mathematics, Faculty of Fundamental Sciences, Moscow State Technical University, Moskva, 2-nd Baumanskaya ul. 5, 105005, Russian Federation, e-mail: flnv@yandex.ru
Abstract: We investigate the spectral properties of the differential operator $-r^s \Delta$, $s\ge0$ 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_{L_{2, s} (\Omega)}= \int_{\Omega} r^{-s} |u|^2 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.
Keywords: Laplace operator, multiplicative perturbation, Dirichlet problem, Friedrichs extension, purely discrete spectra, purely continuous spectra
Classification (MSC 2010): 35J20, 35J25, 35P15
Full text available as PDF.
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
