A note on the scale invariant structure of critical hardy inequalities

Norisuke Ioku, Michinori Ishiwata

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

We investigate the scale-invariant structure of the critical Hardy inequality in a unit ball under the power-type scaling. First we consider the remainder term of the critical Hardy inequality which is characterized by the ratio with or the distance from the “virtual minimizer” for the associated variational problem. We also focus on the scale invariance property of the inequality under power-type scaling and investigate the iterated scaling structure of remainder terms. Finally, we give a relation between the usual scaling enjoyed by the classical Hardy inequality and the power-type scaling via the transformation introduced by Horiuchi and Kumlin. As a by-product, we give a relationship between the Moser sequences and the Talenti functions.

Original languageEnglish
Title of host publicationGeometric Properties for Parabolic and Elliptic PDE’s - GPPEPDEs 2015
EditorsCarlo Nitsch, Filippo Gazzola, Kazuhiro Ishige, Paolo Salani
PublisherSpringer New York LLC
Pages97-120
Number of pages24
ISBN (Print)9783319415369
DOIs
Publication statusPublished - 2016
Externally publishedYes
EventItalian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s, GPPEPDEs 2015 - Palinuro, Italy
Duration: 2015 May 252015 May 29

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume176
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

OtherItalian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s, GPPEPDEs 2015
CountryItaly
CityPalinuro
Period15/5/2515/5/29

Keywords

  • Hardy’s inequality
  • Moser sequences
  • Remainder term
  • Scale invariance
  • Talenti functions

ASJC Scopus subject areas

  • Mathematics(all)

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