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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Singular elliptic operators of second order with purely discrete spectra


Author: Roger T. Lewis
Journal: Trans. Amer. Math. Soc. 271 (1982), 653-666
MSC: Primary 35P05; Secondary 35J25, 47F05
DOI: https://doi.org/10.1090/S0002-9947-1982-0654855-X
MathSciNet review: 654855
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Abstract: The Friedrichs extension of a second order singular elliptic operator is considered on a weighted $ \mathcal{L}_w^2(\Omega )$ space. The region $ \Omega $ is not necessarily bounded. Necessary conditions and sufficient conditions on the coefficients that will insure a discrete spectrum are given with a certain degree of sharpness achieved. The boundary conditions include the Dirichlet, Neumann, and mixed Dirichlet-Neumann boundary value problems.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0654855-X
Article copyright: © Copyright 1982 American Mathematical Society