scholarly journals On a new generalization of some Hilbert-type inequalities

2021 ◽  
Vol 19 (1) ◽  
pp. 569-582
Author(s):  
Minghui You ◽  
Wei Song ◽  
Xiaoyu Wang
Keyword(s):  
Kernel Function ◽  
Euler Number ◽  
Bernoulli Number ◽  
Type Inequality ◽  
Trigonometric Functions ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Higher Derivatives ◽  
Derivatives Of ◽  
Hilbert Type

Abstract In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established. By convention, the equivalent Hardy-type inequality is also considered. Furthermore, by introducing the partial fraction expansions of trigonometric functions, some special and interesting Hilbert-type inequalities with the constant factors represented by the higher derivatives of trigonometric functions, the Euler number and the Bernoulli number are presented at the end of the paper.

A Friedrichs inequality and an application

1984 ◽  
Vol 97 ◽  
pp. 185-191 ◽  
Author(s):  
Roger T. Lewis
Keyword(s):  
Differential Operators ◽  
Arbitrary Order ◽  
Type Inequality ◽  
Essential Spectra ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Partial Differential Operators ◽  
Even Order ◽  
Friedrichs Inequality ◽  
Derivatives Of

SynopsisAn inequality whose origins date to the work of G. H. Hardy is presented. This Hardy-type inequality applies to derivatives of arbitrary order of functions whose domain is a subset of ℝn. The Friedrichs inequality is a corollary. The result is then used to establish lower bounds on the essential spectra of even-order elliptic partial differential operators on unbounded domains.

scholarly journals On a class of Hilbert-type inequalities in the whole plane related to exponent function

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Minghui You
Keyword(s):  
Euler Number ◽  
Bernoulli Number ◽  
Type Inequality ◽  
Partial Fraction ◽  
Multiple Parameters ◽  
Partial Fraction Expansion ◽  
Hilbert Type

AbstractBy introducing a kernel involving an exponent function with multiple parameters, we establish a new Hilbert-type inequality and its equivalent Hardy form. We also prove that the constant factors of the obtained inequalities are the best possible. Furthermore, by introducing the Bernoulli number, Euler number, and the partial fraction expansion of cotangent function and cosecant function, we get some special and interesting cases of the newly obtained 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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