Hardy's inequality and curvature

Academic Article

Abstract

  • A Hardy inequality of the form ∫Ω|∇f(x)|pdx≥(p-1/p)p ∫Ω {1+a(δ,∂Ω)(x)} |f(x)|p/δ(x)p dx, for all f∈C0∞(Ω\R(Ω)), is considered for p∈ (1, ∞), where Ω is a domain in Rn, n≥ 2, R(Ω) is the ridge of Ω, and δ(x) is the distance from x∈ Ω to the boundary ∂ Ω. The main emphasis is on determining the dependence of a(δ, ∂ Ω) on the geometric properties of ∂ Ω. A Hardy inequality is also established for any doubly connected domain Ω in R2 in terms of a uniformization of Ω, that is, any conformal univalent map of Ω onto an annulus. © 2011 Elsevier Inc.
  • Authors

    Published In

    Digital Object Identifier (doi)

    Author List

  • Balinsky A; Evans WD; Lewis RT
  • Start Page

  • 648
  • End Page

  • 666
  • Volume

  • 262
  • Issue

  • 2