scholarly journals Fredholm theory for an elliptic differential operator defined on \begin{document}$ \mathbb{R}^n $\end{document} and acting on generalized Sobolev spaces

2020 ◽  
Vol 19 (3) ◽  
pp. 1463-1483
Author(s):  
Melvin Faierman ◽  
Keyword(s):  
Differential Operator ◽  
Sobolev Spaces ◽  
Fredholm Theory ◽  
Elliptic Differential Operator ◽  
Generalized Sobolev Spaces

Lp-Theory of degenerate-elliptic and parabolic operators of second order

1983 ◽  
Vol 95 (1-2) ◽  
pp. 95-113 ◽  
Author(s):  
Baoswan Wong-Dzung
Keyword(s):  
Banach Space ◽  
Differential Operator ◽  
Positive Semidefinite ◽  
Second Order ◽  
Minimal Realization ◽  
Elliptic Differential Operator ◽  
Second Derivatives ◽  
Degenerate Elliptic ◽  
Image Position ◽  
Lp Theory

SynopsisWe consider the formal operator given byin the Banach space X = LP(Rn), 1<p<∞. The coefficients ajk(x), aj(x), and a(x) are real-valued functions, ajk ε C2(Rn) has bounded second derivatives, aj ε Cl(Rn) has bounded first derivatives, and aεL∞(Rn). Furthermore, we assume that the n × n matrix (ajk(x)) is symmetric and positive semidefinite (i.e. ajk(x)ξjξk≧0 for all (ξ1,…,ξn)ε Rn and x ε Rn). We prove that the degenerate-elliptic differential operator given by –A and restricted to , the minimal realization of –A, is essentially quasi-m-dispersive in Lp(Rn), (hence that the minimal realization of +A is quasi-m-accretive) and that its closure coincides with the maximal realization of –A.

Sign in / Sign up

Export Citation Format

Share Document