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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.

Information

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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