Sharp Sobolev inequality of logarithmic type and the limiting regularity condition to the harmonic heat flow

Takayoshi Ogawa

Research output: Contribution to journalArticle

40 Citations (Scopus)

Abstract

We show a sharp version of the Sobolev inequality of the Beale-Kato-Majda and the Kozono-Taniuchi type in Lizorkin-Triebel space. As an application of this inequality, the regularity problem under the critical condition to the gradient flow of the harmonic map into a sphere is considered in the class L2(0, T; BMO(ℝn;struck S sign m)), where BMO is the class of functions of bounded mean oscillations.

Original languageEnglish
Pages (from-to)1318-1330
Number of pages13
JournalSIAM Journal on Mathematical Analysis
Volume34
Issue number6
DOIs
Publication statusPublished - 2003 Nov 20
Externally publishedYes

Keywords

  • Bounded mean oscillation
  • Critical Sobolev inequalities
  • Harmonic heat flow
  • Interpolation inequality
  • Lizorkin-Triebel space
  • Regularity criterion

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Sharp Sobolev inequality of logarithmic type and the limiting regularity condition to the harmonic heat flow'. Together they form a unique fingerprint.

  • Cite this