Hardy's inequality and curvature

Balinsky, Alexander ORCID: https://orcid.org/0000-0002-8151-4462, Evans, William Desmond and Lewis, R. T. 2012. Hardy's inequality and curvature. Journal of Functional Analysis 262 (2) , pp. 648-666. 10.1016/j.jfa.2011.10.001

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Abstract

A Hardy inequality of the form ∫Ω|∇f(x)|pdx⩾(p−1p)p∫Ω{1+a(δ,∂Ω)(x)}|f(x)|pδ(x)pdx,for all f∈C0∞(Ω∖R(Ω)), is considered for p∈(1,∞)p∈(1,∞), where Ω is a domain in RnRn, n⩾2n⩾2, R(Ω)R(Ω) is the ridge of Ω, and δ(x)δ(x) is the distance from x∈Ωx∈Ω to the boundary ∂Ω. The main emphasis is on determining the dependence of a(δ,∂Ω)a(δ,∂Ω) on the geometric properties of ∂Ω. A Hardy inequality is also established for any doubly connected domain Ω in R2R2 in terms of a uniformization of Ω, that is, any conformal univalent map of Ω onto an annulus.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Hardy inequality; Distance function; Curvature; Ridge; Skeleton; Uniformization
Publisher:	Elsevier
ISSN:	0022-1236
Last Modified:	21 Oct 2022 09:36
URI:	https://orca.cardiff.ac.uk/id/eprint/37049

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