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

Abstract

SynopsisLet τ denote the second-order elliptic expressionwhere 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.