scholarly journals On the Logarithmic Regularity Conditions for the Variable Exponent Hardy Type Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Aziz Harman ◽  
Mustafa Özgür Keleş
Keyword(s):  
Hardy Inequality ◽  
Variable Exponent ◽  
Regularity Condition ◽  
Type Inequality ◽  
Regularity Conditions ◽  
Hardy Type Inequality ◽  
Hardy Type

We discuss a logarithmic regularity condition in a neighborhood of the origin and infinity on the exponent functions qx≥px and βx for the variable exponent Hardy inequality xβ·-1∫0xftdtLp·0,l≤Cxβ·fLp·0,l to hold.

scholarly journals Fractional Korn and Hardy-type inequalities for vector fields in half space

2019 ◽  
Vol 21 (07) ◽  
pp. 1850055 ◽  
Author(s):  
Tadele Mengesha
Keyword(s):  
Half Space ◽  
Hardy Inequality ◽  
Vector Fields ◽  
A Priori ◽  
Type Inequality ◽  
Fractional Sobolev Spaces ◽  
Hardy Type Inequality ◽  
Hardy Type Inequalities ◽  
Korn’S Inequality ◽  
Hardy Type

We prove a fractional Hardy-type inequality for vector fields over the half space based on a modified fractional semi-norm. A priori, the modified semi-norm is not known to be equivalent to the standard fractional semi-norm and in fact gives a smaller norm, in general. As such, the inequality we prove improves the classical fractional Hardy inequality for vector fields. We will use the inequality to establish the equivalence of a space of functions (of interest) defined over the half space with the classical fractional Sobolev spaces, which amounts to prove a fractional version of the classical Korn’s inequality.

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 Eigencurves of the p(·)-Biharmonic operator with a Hardy-type term

2020 ◽  
Vol 6 (2) ◽  
pp. 198-209
Author(s):  
Mohamed Laghzal ◽  
Abdelouahed El Khalil ◽  
My Driss Morchid Alaoui ◽  
Abdelfattah Touzani
Keyword(s):  
Dirichlet Problem ◽  
Variational Approach ◽  
Type Inequality ◽  
Biharmonic Operator ◽  
Nondecreasing Sequence ◽  
Hardy Type Inequality ◽  
Principal Curve ◽  
Hardy Type ◽  
Homogeneous Dirichlet Problem

AbstractThis paper is devoted to the study of the homogeneous Dirichlet problem for a singular nonlinear equation which involves the p(·)-biharmonic operator and a Hardy-type term that depend on the solution and with a parameter λ. By using a variational approach and min-max argument based on Ljusternik-Schnirelmann theory on C1-manifolds [13], we prove that the considered problem admits at least one nondecreasing sequence of positive eigencurves with a characterization of the principal curve μ1(λ) and also show that, the smallest curve μ1(λ) is positive for all 0 ≤ λ < CH, with CH is the optimal constant of Hardy type inequality.

Degenerate p-Laplacian Operators and Hardy Type Inequalities on H-Type Groups

2010 ◽  
Vol 62 (5) ◽  
pp. 1116-1130 ◽  
Author(s):  
Yongyang Jin ◽  
Genkai Zhang
Keyword(s):  
Vector Fields ◽  
Orthonormal Basis ◽  
Type Inequality ◽  
Laplacian Operator ◽  
Hardy Type Inequality ◽  
Invariant Vector ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Left Invariant Vector ◽  
Laplacian Operators

AbstractLet 𝔾 be a step-two nilpotent group of H-type with Lie algebra 𝔊 = V ⊕ t. We define a class of vector fields X = {Xj} on 𝔾 depending on a real parameter k ≥ 1, and we consider the corresponding p-Laplacian operator Lp,ku = divX(|∇Xu|p−2∇Xu). For k = 1 the vector fields X = {Xj} are the left invariant vector fields corresponding to an orthonormal basis of V; for 𝔾 being the Heisenberg group the vector fields are the Greiner fields. In this paper we obtain the fundamental solution for the operator Lp,k and as an application, we get a Hardy type inequality associated with X.

General Hardy type inequality for seminormed fuzzy integrals

2010 ◽  
Vol 216 (7) ◽  
pp. 1972-1977 ◽  
Author(s):  
Hamzeh Agahi ◽  
M.A. Yaghoobi
Keyword(s):  
Type Inequality ◽  
Hardy Type Inequality ◽  
Hardy Type

A weighted Hardy type inequality and its applications

2021 ◽  
Vol 166 ◽  
pp. 102937
Author(s):  
Emerson Abreu ◽  
Diego Dias Felix ◽  
Everaldo Medeiros
Keyword(s):  
Type Inequality ◽  
Hardy Type Inequality ◽  
Hardy Type
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