Continuity in Weighted Sobolev Spaces Of Lp Type for Pseudo-Differential Operators with Completely Nonsmooth Symbols

2004 ◽  
pp. 91-106 ◽  
Author(s):  
Gianluca Garello ◽  
Alessandro Morando
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Pseudo Differential Operators

scholarly journals Pseudo-monotonicity and degenerated or singular elliptic operators

1998 ◽  
Vol 58 (2) ◽  
pp. 213-221 ◽  
Author(s):  
P. Drábek ◽  
A. Kufner ◽  
V. Mustonen
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Type Inequality ◽  
Elliptic Operators ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Elliptic Differential Operators

Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The result extends analogous assertions for elliptic operators.

scholarly journals THE DISCRETENESS OF SPECTRUM FOR HIGHER-ORDER DIFFERENTIAL OPERATORS IN WEIGHTED FUNCTION SPACES

2012 ◽  
Vol 86 (3) ◽  
pp. 370-376
Author(s):  
MAOZHU ZHANG ◽  
JIONG SUN ◽  
JIJUN AO
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Function Spaces ◽  
Higher Order ◽  
Necessary Condition ◽  
Embedding Theorems ◽  
Weighted Function ◽  
Weighted Function Spaces ◽  
Sufficient And Necessary Condition

AbstractIn this paper we consider the discreteness of spectrum for higher-order differential operators in weighted function spaces. Using the method of embedding theorems of weighted Sobolev spaces Hnp in weighted spaces Ls,r, we obtain a new sufficient and necessary condition to ensure that the spectrum is discrete, which can be easily used to judge the discreteness of some differential operators.

scholarly journals A Priori Bounds for a Class of Elliptic Operators

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Sara Monsurrò ◽  
Maria Salvato ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Existence Theorem ◽  
Sobolev Spaces ◽  
Differential Operators ◽  
A Priori ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Elliptic Operators ◽  
A Priori Bounds ◽  
Uniqueness And Existence

We obtain some a priori bounds for a class of uniformly elliptic second-order differential operators, both in a no-weighted and in a weighted case. We deduce a uniqueness and existence theorem for the related Dirichlet problem in some weighted Sobolev spaces on unbounded domains.

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