A homothety argument for computing the best constant in some Hardy's inequalities for exterior and punctured domains

by Shayne Waldron

Abstract:

An argument based on homothety transformations is used to prove a conjecture about multivariate Hardy's inequalities of Matskewich and Sobolevskii [MS96]. This result and more general inequalities are seen to follow from a multivariate form of Hardy's inequality recently given in Waldron [W97].

Keywords: Hardy's inequality, homothety transformation, integral form of Minkowskii's inequality, Sobolev's embedding theorem, Taylor interpolation

Math Review Classification: 26D10, 41A44 (primary), 41A80 (secondary)

Length: 7 pages

Comment: Written in TeX. I was invited by Simeon Reich to write this article for the conference proceedings of the Special Session on Optimization and Nonlinear Analysis which was a part of the Joint American Mathematical Society - Israel Mathematical Union Meeting which took place in Jerusalem in May of 1995.

Last updated: 20 July 1997

Status: To be submitted

Availability:

This article is available in: