Singular elliptic operators of second order with purely discrete spectra

Lewis, Roger T.

doi:10.1090/S0002-9947-1982-0654855-X

Singular elliptic operators of second order with purely discrete spectra
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Trans. Amer. Math. Soc. 271 (1982), 653-666 Request permission

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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