scholarly journals THE IDENTITY OF THE WEAK AND STRONG EXTENSIONS OF A LINEAR ELLIPTIC DIFFERENTIAL OPERATOR: II

1957 ◽  
Vol 43 (7) ◽  
pp. 620-620
Author(s):  
M. S. Narasimhan
Keyword(s):  
Differential Operator ◽  
Elliptic Differential Operator ◽  
Linear Elliptic Differential Operator

scholarly journals An inverse mapping theorem for Sobolev chains and its application

1983 ◽  
Vol 27 (3) ◽  
pp. 381-394
Author(s):  
Truong Công Nghê
Keyword(s):  
Differential Operator ◽  
Solution Space ◽  
Elliptic Differential Operator ◽  
Inverse Mapping ◽  
Inverse Mapping Theorem ◽  
Non Linear ◽  
Smooth Coefficients ◽  
Finite Dimensionality ◽  
Linear Elliptic Differential Operator

The author combines the methods used by Yamamuro and Omori to define a differentiation in Sobolev chains and obtain an Inverse Mapping Theorem. He then uses this theorem to give a new proof for a result of Sunada on the local finite-dimensionality of the solution space of a non-linear elliptic differential operator with smooth coefficients.

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.

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