Anisotropic equations in weighted Sobolev spaces of higher order

2009 ◽  
Vol 58 (1) ◽  
pp. 1-14 ◽  
Author(s):  
M. Chrif ◽  
S. El Manouni
Keyword(s):  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Higher Order

A Sharp Adams-Type Inequality for Weighted Sobolev Spaces

2020 ◽  
Vol 71 (2) ◽  
pp. 517-538
Author(s):  
João Marcos do Ó ◽  
Abiel Costa Macedo ◽  
José Francisco de Oliveira
Keyword(s):  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Type Inequality ◽  
Higher Order ◽  
Sobolev Type ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Classical Work

Abstract In a classical work (Ann. Math.128, (1988) 385–398), D. R. Adams proved a sharp Trudinger–Moser inequality for higher-order derivatives. We derive a sharp Adams-type inequality and Sobolev-type inequalities associated with a class of weighted Sobolev spaces that is related to a Hardy-type inequality.

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.

Elliptic equations of higher-order in weighted Sobolev spaces

2013 ◽  
Vol 25 (3) ◽  
pp. 645-665
Author(s):  
E. Azroul ◽  
A. Benkirane ◽  
H. Redwane ◽  
M. Rhoudaf
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Weighted Sobolev Spaces ◽  
Higher Order

Weighted higher order exponential type inequalities in metric spaces and applications

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huiju Wang ◽  
Pengcheng Niu
Keyword(s):  
Homogeneous Space ◽  
Lie Groups ◽  
Sobolev Spaces ◽  
Exponential Type ◽  
Metric Spaces ◽  
Type Inequality ◽  
Higher Order ◽  
Geodesic Space ◽  
Stratified Lie Groups ◽  
Weighted Case

AbstractIn this paper, we establish weighted higher order exponential type inequalities in the geodesic space {({X,d,\mu})} by proposing an abstract higher order Poincaré inequality. These are also new in the non-weighted case. As applications, we obtain a weighted Trudinger’s theorem in the geodesic setting and weighted higher order exponential type estimates for functions in Folland–Stein type Sobolev spaces defined on stratified Lie groups. A higher order exponential type inequality in a connected homogeneous space is also given.

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.

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