Sharp remainder terms of Hardy-Sobolev inequalities

• DETALLA ALNAR

  Deepartment of Mathematics, College of Arts and Sciences, Central Mindanao University

• HORIUCHI TOSHIO

  Department of Mathematical Sciences, Ibaraki University

• ANDO HIROSHI

  Department of Mathematical Sciences, Ibaraki University

Abstract

In this paper we shall prove the existence of sharp remainder terms involving singular weight (logR/|x|)^-2 for Hardy-Sobolev inequalities of the following type:<br>∫_Ω|∇u(x)|²dx≥(n-2/2)²∫_Ω|u(x)|²/|(x)|²dx for any u∈W^{1, 2}₀(Ω), Ω is a bounded domain in Rⁿ, n>2, with 0∈Ω. Here the number of remainder terms depends on the choice of R.

Journal

• Mathematical Journal of Ibaraki University

  Mathematical Journal of Ibaraki University 37 39-52, 2005

  Department of Mathematics, Faculty of Science, Ibaraki University

Details

• CRID: 1390282680252775296
• NII Article ID: 130000886481
• NII Book ID: AA11169155
• DOI: 10.5036/mjiu.37.39
• ISSN: 18834353
• ISSN: 13433636
• MRID: 2207669
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed