Related papers: Discrete Weighted Hardy Inequalities with Differen…
This paper studies the Hardy-type inequalities on the discrete intervals. The first result is the variational formulas of the optimal constants. Using these formulas, one may obtain an approximating procedure and the known basic estimates…
In the present paper we shall establish n-dimensional Hardy's inequalities with non-doubling weight functions of the distance to the boundary, where the boundary is a $C^2$ class bounded domain of $R^N$. This work is essentially based on…
This paper studies the Hardy-type inequalities on the intervals (may be infinite) with two weights, either vanishing at two endpoints of the interval or having mean zero. For the first type of inequalities, in terms of new isoperimetric…
We study finite sections of weighted Hardy's inequality following the approach of De Bruijn. Similar to the unweighted case, we obtain an asymptotic expression for the optimal constant.
Let $\O$ be a smooth bounded domain in $\R^N$ with $N\ge 1$. In this paper we study the Hardy-Poincar\'e inequalities with weight function singular at the boundary of $\O$. In particular we give sufficient conditions so that the best…
We consider weighted Hardy inequalities involving the distance function to the boundary of a domain in the $N$-dimensional Euclidean space with nonempty boundary. We give a lower bound for the corresponding best Hardy constant for a domain…
In the present paper we shall improve one dimensional weighted Hardy inequalities with one-sided boundary condition by adding sharp remainders. As an application, we shall establish n dimensional weighted Hardy inequalities in a bounded…
In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms. As weights we treat non-doubling functions of the distance to the boundary of bounded domain.
We revisit weighted Hardy-type inequalities employing an elementary ad hoc approach that yields explicit constants. We also discuss the infinite sequence of power weighted Birman-Hardy-Rellich-type inequalities and derive an operator-valued…
The aim of this paper is to obtain new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain. These inequalities give us the possibility to derive estimates from below of the first…
To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is…
We study some Hardy-type inequalities involving a general norm in $R^n$ and an anisotropic distance function to the boundary. The case of the optimality of the constants is also addressed.
We prove sharp homogeneous improvements to $L^1$ weighted Hardy inequalities involving distance from the boundary. In the case of a smooth domain, we obtain lower and upper estimates for the best constant of the remainder term. These…
We study the Hardy inequality when the singularity is placed on the boundary of a bounded domain in $\mathbb{R}^n$ that satisfies both an interior and exterior ball condition at the singularity. We obtain the sharp Hardy constant $n^2/4$ in…
In this paper, we establish a general weighted Hardy type inequality for the $% p-$Laplace operator with Robin boundary condition. We provide various concrete examples to illustrate our results for different weights. Furthermore, we present…
In this paper, we establish discrete Hardy-Rellich inequalities on $\mathbb{N}$ with $\Delta^\frac{\ell}{2}$ and optimal constants, for any $\ell \geq 1$. As far as we are aware, these sharp inequalities are new for $\ell \geq 3$. Our…
The objective of the present paper is to establish three Hardy-type inequalities in which the arithmetic mean over a sequence of non-negative real numbers is replaced by some weighted arithmetic mean over some nested subsets of the given…
Boundary value problems for non-linear parabolic equations with singular potentials are considered. Existence and non-existence results as an application of different Hardy inequalities are proved. Blow-up conditions are investigated too.
We present a theory for constructing optimal lower bounds for the discrete half-line $p$-Laplacian of higher order $\ell\in\mathbb{N}$ and general $p>1$. The abstract framework introduces higher-order monotonicity and asymptotic constraints…
We study weighted inequalities of Hardy and Hardy-Poincar\'e type and find necessary and sufficient conditions on the weights so that the considered inequalities hold. Examples with the optimal constants are shown. Such inequalities are…