A note on the scale invariant structure of critical hardy inequalities

Norisuke Ioku, Michinori Ishiwata

研究成果: Conference contribution

4 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトルGeometric Properties for Parabolic and Elliptic PDE’s - GPPEPDEs 2015
編集者Carlo Nitsch, Filippo Gazzola, Kazuhiro Ishige, Paolo Salani
出版社Springer New York LLC
ページ97-120
ページ数24
ISBN(印刷版)9783319415369
DOI
出版ステータスPublished - 2016
外部発表はい
イベントItalian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s, GPPEPDEs 2015 - Palinuro, Italy
継続期間: 2015 5月 252015 5月 29

出版物シリーズ

名前Springer Proceedings in Mathematics and Statistics
176
ISSN(印刷版)2194-1009
ISSN(電子版)2194-1017

Other

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

ASJC Scopus subject areas

  • 数学 (全般)

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