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

被引：41

作者：

Ogawa, T ^{[1
]}

机构：

[1] Kyushu Univ 36, Fac Math, Fukuoka 8128581, Japan

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2003年 / 34卷 / 06期

关键词：

critical Sobolev inequalities; Lizorkin-Triebel space; interpolation inequality; harmonic heat flow; regularity criterion; bounded mean oscillation;

D O I：

10.1137/S0036141001395868

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 L-2(0, T; BMO(R-n; S-m)), where BMO is the class of functions of bounded mean oscillations.

引用

页码：1318 / 1330

页数：13

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