A geometric characterization of a sharp Hardy inequality

作者：Lewis Roger T; Li Junfang^*; Li Yanyan

来源：Journal of Functional Analysis, 2012, 262(7): 3159-3185.

DOI：10.1016/j.jfa.2012.01.015

• Distance function
• Superharmonic
• Hardy inequality

In this paper, we prove that the distance function of an open connected set in Rn+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]. Published by Elsevier Inc.

• 出版日期2012-4-1
• 单位rutgers