scholarly journals Optimal Hardy-weights for the (p, A)-Laplacian with a potential term

2021 ◽  
pp. 1-18
Author(s):  
Idan Versano
Keyword(s):  
Potential Term ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Schrödinger Type Operators

We construct new optimal $L^{p}$ Hardy-type inequalities for elliptic Schrödinger-type operators with a potential term.

Compactness properties of critical nonlinearities and nonlinear Schrödinger equations

2013 ◽  
Vol 56 (2) ◽  
pp. 427-441 ◽  
Author(s):  
David G. Costa ◽  
João Marcos do Ó ◽  
K. Tintarev
Keyword(s):  
Sobolev Norm ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Pointwise Estimates ◽  
Potential Term ◽  
Hardy Type Inequalities ◽  
Sobolev Embeddings ◽  
Hardy Type ◽  
Broad Array ◽  
Type Potential

AbstractWe prove the compactness of critical Sobolev embeddings with applications to nonlinear singular Schrödinger equations and provide a unified treatment in dimensions N > 2 and N = 2, based on a somewhat unexpectedly broad array of parallel properties between spaces $\smash{\mathcal{D}^{1,2}(\mathbb{R}^N)}$ and H10 of the unit disc. These properties include Leray inequality for N = 2 as a counterpart of Hardy inequality for N > 2, pointwise estimates by ground states r(2−N)/2 and $\smash{\sqrt{\log(1/r)}}$ of the respective Hardy-type inequalities, as well as compactness of the limiting Sobolev embeddings once the Sobolev norm is appended by a potential term whose growth at singularities exceeds that of the corresponding Hardy-type potential.

scholarly journals Some new Hardy-type inequalities on time scales

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ahmed A. El-Deeb ◽  
Hamza A. Elsennary ◽  
Dumitru Baleanu
Keyword(s):  
Time Scales ◽  
Hardy Type Inequalities ◽  
Hardy Type

On Hardy-Type Inequalities

1998 ◽  
Vol 194 (1) ◽  
pp. 23-33 ◽  
Author(s):  
D. E. Edmunds ◽  
R. Hurri-Syrjänen
Keyword(s):  
Hardy Type Inequalities ◽  
Hardy Type

On some Hardy-type inequalities for fractional calculus operators

2017 ◽  
Vol 11 (2) ◽  
pp. 438-457 ◽  
Author(s):  
Sajid Iqbal ◽  
Josip Pečarić ◽  
Muhammad Samraiz ◽  
Zivorad Tomovski
Keyword(s):  
Fractional Calculus ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Fractional Calculus Operators

scholarly journals Hardy-Type Inequalities for an Extension of the Riemann- Liouville Fractional Derivative Operators

2021 ◽  
Vol 45 (5) ◽  
pp. 797-813
Author(s):  
SAJID IQBAL ◽  
◽  
GHULAM FARID ◽  
JOSIP PEČARIĆ ◽  
ARTION KASHURI
Keyword(s):  
Fractional Derivative ◽  
Convex Functions ◽  
Mean Value ◽  
Mean Value Theorems ◽  
Hardy Type Inequalities ◽  
Exponential Convexity ◽  
Hardy Type ◽  
Liouville Fractional Derivative ◽  
Fractional Derivative Operators

In this paper we present variety of Hardy-type inequalities and their refinements for an extension of Riemann-Liouville fractional derivative operators. Moreover, we use an extension of extended Riemann-Liouville fractional derivative and modified extension of Riemann-Liouville fractional derivative using convex and monotone convex functions. Furthermore, mean value theorems and n-exponential convexity of the related functionals is discussed.

scholarly journals Some Hardy-Type Inequalities for Superquadratic Functions via Delta Fractional Integrals

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Usama Hanif ◽  
Ammara Nosheen ◽  
Rabia Bibi ◽  
Khuram Ali Khan ◽  
Hamid Reza Moradi
Keyword(s):  
Fractional Calculus ◽  
Time Scales ◽  
Fractional Integrals ◽  
Discrete Fractional Calculus ◽  
Hardy Inequalities ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Superquadratic Functions

In this paper, Jensen and Hardy inequalities, including Pólya–Knopp type inequalities for superquadratic functions, are extended using Riemann–Liouville delta fractional integrals. Furthermore, some inequalities are proved by using special kernels. Particular cases of obtained inequalities give us the results on time scales calculus, fractional calculus, discrete fractional calculus, and quantum fractional calculus.

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