Related papers: A note on Hardy's inequalities with boundary singu…

Let $\O$ be a smooth bounded domain in $\R^N$ with $N\ge 1$. In this paper we study the Hardy-Poincar\'e inequality with weight function singular at the boundary of $\O$. In particular we provide sufficient and necessary conditions on the…

Let $\O$ be a bounded domain in $\R^N$ with $0\in\de\O$ and $N\ge 2$. In this paper we study the Hardy-Poincar\'e inequality for maps in $H^1_0(\Omega)$. In particular we give sufficient and some necessary conditions so that the best…

In this work we prove some Hardy-Poincar\'{e} inequalities with quadratic singular potentials localized on the boundary of a smooth domain. Then, we consider conical domains with vertex on the singularity and we show upper and lower bounds…

Let $\Omega$ be a smooth bounded domain in $\mahbb R^N$ with $N\ge 3$ and let $\Sigma_k$ be a closed smooth submanifold of $\delta \Omega$ of dimension $1\le k\le N-2$. In this paper we study the weighted Hardy inequality with weight…

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…

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…

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…

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…

We consider a type of Hardy-Sobolev inequality, whose weight function is singular on the whole domain boundary. We are concerned with the attainability of the best constant of such inequality. In dimension two, we link the inequality to a…

We establish fractional Hardy inequality on bounded domains in $\mathbb{R}^{d}$ with inverse of distance function from smooth boundary of codimension $k$, where $k=2, \dots,d$, as weight function. The case $sp=k$ is the critical case, where…

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…

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…

Let $\Omega$ be a bounded domain of $\mathbb{R}^N$ whose boundary is a $\mathbb{C}^2$ compact manifolds. In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms. As weights…

We consider the Schr\"{o}dinger operator $A_\l:=-\D -\l/|x|^2$, $\l\in \rr$, when the singularity is located on the boundary of a smooth domain $\Omega\subset \rr^N$, $N\geq 1$ The aim of this Note is two folded. Firstly, we justify the…

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.

This paper studies the weighted Hardy inequalities on the discrete intervals with four different kinds of boundary conditions. The main result is the uniform expression of the basic estimate of the optimal constant with the corresponding…

We develop a geometric framework for Hardy's inequality on a bounded domain when the functions do vanish only on a closed portion of the boundary.

We prove a sharp upper bound on convex domains, in terms of the diameter alone, of the best constant in a class of weighted Poincar\'e inequalities. The key point is the study of an optimal weighted Wirtinger inequality.

In this paper, we study certain inequalities and a related result for weighted Sobolev spaces on H\"older-$\alpha$ domains, where the weights are powers of the distance to the boundary. We obtain results regarding the divergence equation's…

For a bounded convex domain \Omega in R^N we prove refined Hardy inequalities that involve the Hardy potential corresponding to the distance to the boundary of \Omega, the volume of $\Omega$, as well as a finite number of sharp logarithmic…