Related papers: Anisotropic Hardy inequalities

We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type inequality that takes…

We study a class of Riemannian manifolds which are equipped with a singular metric. In particular we study a domain perturbation problem for the Dirichlet eigenvalues which depends on the best constant in the Hardy Inequality. However, we…

We obtain a differential characterization for the anisotropic Hardy space $H_A^p$ by identifying it with a parabolic Hardy space associated with a general continuous group. This allows $H_A^p$ to be defined using a parabolic differential…

In this article, we investigate electrostatic systems with a nonzero cosmological constant on compact manifolds with boundary. We establish new geometric properties for electrostatic manifolds in higher dimensions, extending previous…

This paper studies sharp and rigid isoperimetric comparison theorems and asymptotic isoperimetric properties for small and large volumes on $N$-dimensional ${\rm RCD}(K,N)$ spaces $(X,\mathsf{d},\mathscr{H}^N)$. Moreover, we obtain almost…

We study the Schr\"odinger-Robertson uncertainty relations in an algebraic framework. Moreover, we show that some specific commutation relations imply new equalities, which are regarded as equality versions of well-known inequalities such…

We consider a finite horizon linear discrete time varying system whose input is a random noise with an imprecisely known probability law. The statistical uncertainty is described by a nonnegative parameter a which constrains the anisotropy…

We construct new examples of complete Einstein metrics on balls. At each point of the boundary at infinity, the metric is asymptotic to a homogeneous Einstein metric on a solvable group, which varies with the point at infinity.

In this article we first establish a complete characterization of Hardy's inequalities in $\mathbb{R}^n$ involving distances to different codimension subspaces. In particular the corresponding potentials have strong interior singularities.…

We give a characterization of transport-entropy inequalities in metric spaces. As an application we deduce that such inequalities are stable under bounded perturbation (Holley-Stroock perturbation Lemma).

In this paper we state the weighted Hardy inequality \begin{equation*} c\int_{{\mathbb R}^N}\sum_{i=1}^n \frac{\varphi^2 }{|x-a_i|^2}\, \mu(x)dx\le \int_{{\mathbb R}^N} |\nabla\varphi|^2 \, \mu(x)dx +k \int_{\mathbb{R}^N}\varphi^2 \,…

We present an easy proof that $p$--Hardy's inequality implies uniform $p$--fatness of the boundary when $p=n$. The proof works also in metric space setting and demonstrates the self--improving phenomenon of the $p$--fatness. We also explore…

We present simple proofs of a discrete fractional and non-fractional Hardy inequality, Our constants are explicit, but not optimal. In the class of power weights, we get a complete picture of when the non-fractional Hardy inequality holds,…

Various properties of isoperimetric, functional, Transport-Entropy and concentration inequalities are studied on a Riemannian manifold equipped with a measure, whose generalized Ricci curvature is bounded from below. First, stability of…

We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…

We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are…

In this article, we consider Einstein-type manifolds with boundary which generalizes important geometric equations, like static vacuum and static perfect fluid. We investigate some geometric inequalities for those manifolds. Then, we…

We consider finite element approximations to the optimal constant for the Hardy inequality with exponent $p=2$ in bounded domains of dimension $n=1$ or $n \geq 3$. For finite element spaces of piecewise linear and continuous functions on a…

This paper examines the general formalism and applications of isotropic as well as anisotropic polytropic stars in curvature-matter coupled gravity. For this purpose, we consider static spherical and Schwarzschild spacetimes in the interior…

In this paper, we introduce a symmetrization technique for the distributional gradient of a function of bounded variation in the anisotropic setting. This generalizes the result obtained in the Euclidean case in…