Some results on second-order elliptic operators with polynomially growing coefficients in L-spaces

2021 ◽  
pp. 125209
Author(s):  
Sallah Eddine Boutiah ◽  
Loredana Caso ◽  
Federica Gregorio ◽  
Cristian Tacelli
Keyword(s):  
Elliptic Operators ◽  
Second Order ◽  
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.

Homogeneous Calderón–Zygmund estimates for a class of second-order elliptic operators

2014 ◽  
Vol 17 (01) ◽  
pp. 1450017 ◽  
Author(s):  
G. P. Galdi ◽  
G. Metafune ◽  
C. Spina ◽  
C. Tacelli
Keyword(s):  
Elliptic Operator ◽  
Unique Solvability ◽  
Elliptic Operators ◽  
Second Order ◽  
Poisson Problem ◽  
Second Order Elliptic Operators ◽  
Uniformly Continuous

We prove unique solvability and corresponding homogeneous Lp estimates for the Poisson problem associated to the uniformly elliptic operator [Formula: see text], provided the coefficients are bounded and uniformly continuous, and admit a (non-zero) limit as |x| goes to infinity. Some important consequences are also derived.

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