Fundamental Solutions for Second Order Elliptic Operators in Clifford-Type Algebras

2014 ◽  
Vol 25 (3) ◽  
pp. 527-538 ◽  
Author(s):  
Eusebio Ariza ◽  
Antonio Di Teodoro ◽  
Adrián Infante ◽  
Judith Vanegas
Keyword(s):  
Fundamental Solutions ◽  
Elliptic Operators ◽  
Second Order ◽  
Clifford Type Algebras ◽  
Second Order Elliptic Operators

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

1981 ◽  
Vol 90 (1-2) ◽  
pp. 71-105 ◽  
Author(s):  
W. D. Evans
Keyword(s):  
Spherical Shell ◽  
Essential Spectrum ◽  
Weighted Space ◽  
Elliptic Operators ◽  
Second Order ◽  
Sectorial Operator ◽  
Image Position ◽  
Second Order Elliptic Operators ◽  
Complex Valued

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.

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