A geometric characterization of a sharp Hardy inequality

Academic Article

Abstract

  • In this paper, we prove that the distance function of an open connected set in R n+1 with a C 2 boundary is superharmonic in the distribution sense if and only if the boundary is weakly mean convex. We then prove that Hardy inequalities with a sharp constant hold on weakly mean convex C 2 domains. Moreover, we show that the weakly mean convexity condition cannot be weakened. We also prove various improved Hardy inequalities on mean convex domains along the line of Brezis and Marcus (1997) [7]. © 2012.
  • Published In

    Digital Object Identifier (doi)

    Author List

  • Lewis RT; Li J; Li Y
  • Start Page

  • 3159
  • End Page

  • 3185
  • Volume

  • 262
  • Issue

  • 7