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On the spectra of non-self-adjoint realisations of second-order elliptic operators

Published online by Cambridge University Press:  14 November 2011

W. D. Evans
W. D. Evans
Affiliation:
Pure Mathematics Department, University College, Cardiff
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Synopsis

Let τ denote the second-order elliptic expression

where the coefficients bj and q are complex-valued, and let Ω be a spherical shell Ω = {x:x ∈ ℝn, l <|x|<m} with l≧0, m≦∞. Under the conditions assumed on the coefficients of τ and with either Dirichlet or Neumann conditions on the boundary of Ω, τ generates a quasi-m-sectorial operator T in the weighted space L2(Ω;w). The main objective is to locate the spectrum and essential spectrum of T. Best possible results are obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 90 , Issue 1-2 , 1981 , pp. 71 - 105
Copyright
Copyright © Royal Society of Edinburgh 1981

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