We study the kernel function of the operator u↦ L μ u=− Δ u+ μ| x| 2 u in a bounded smooth
domain Ω⊂ R+ N such that 0∈∂ Ω, where μ≥− N 2 4 is a constant. We show the existence …

Abstract Let\(\Omega\subset {\mathbb {R}}^ N\)(\(N\ge 3\)) be a bounded\(C^ 2\) domain
and\(\Sigma\subset\partial\Omega\) be a compact\(C^ 2\) submanifold of dimension k …

Let Ω be a bounded domain in RN with C 2 boundary and let K⊂∂ Ω be either a C 2
submanifold of the boundary of codimension k< N or a point. In this article we study various …

We study existence and uniqueness of solutions of (E 1)− Δ u+ μ| x| 2 u+ g (u)= ν in Ω, u= λ
on∂ Ω, where Ω⊂ ℝ+ N is a bounded smooth domain such that 0∈∂ Ω, μ≥− N 2 4 is a …

The principal aim of this paper is to extend Birman's sequence of integral inequalities
originally obtained in Mat. Sb.(NS) 55 (97), 125–174,(1961), and containing Hardy's and …

This book derives new Hardy inequalities with double singular weights-at an interior point
and on the boundary of the domain. We focus on the optimality of Hardy constant and on its …

The principal aim of this paper is to establish the optimality (ie, sharpness) of the constants A
(m, α) and B (m, α), m∈ ℕ, α∈ ℝ, of the form in the power-weighted Birman-Hardy-Rellich …

Optimal Hardy-weights for the (p, A)-Laplacian with a potential term Page 1 Proceedings of the
Royal Society of Edinburgh, 153, 289–306, 2023 DOI:10.1017/prm.2021.85 Optimal …

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 …

We develop a unified strategy to obtain the geometric logarithmic Hardy inequality on any
open set M of a stratified group, provided the validity of the Hardy inequality in this setting …