Sharp remainder terms of Hardy-Sobolev inequalities Sharp remainder terms of Hardy-Sobolev inequalities

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Author(s)

    • DETALLA ALNAR
    • Deepartment of Mathematics, College of Arts and Sciences, Central Mindanao 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 (log<i>R</i>/|<i>x</i>|)<sup>-2</sup> for Hardy-Sobolev inequalities of the following type:<br>∫<sub>Ω</sub>|∇<i>u</i>(<i>x</i>)|<sup>2</sup><i>dx</i>≥(<i>n</i>-2/2)<sup>2</sup>∫<sub>Ω</sub>|<i>u</i>(<i>x</i>)|<sup>2</sup>/|(<i>x</i>)|<sup>2</sup><i>dx</i> for any <i>u</i>∈<i>W</i><sup>1, 2</sup><sub>0</sub>(Ω), Ω is a bounded domain in R<sup><i>n</i></sup>, <i>n</i>>2, with 0∈Ω. Here the number of remainder terms depends on the choice of <i>R</i>.

Journal

  • Mathematical Journal of Ibaraki University

    Mathematical Journal of Ibaraki University (37), 39-52, 2005

    Faculty of Science, Ibaraki University

Codes

  • NII Article ID (NAID)
    130000886481
  • NII NACSIS-CAT ID (NCID)
    AA11169155
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    1343-3636
  • Data Source
    IR  J-STAGE 
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