TY - JOUR
T1 - Sharp Sobolev inequality of logarithmic type and the limiting regularity condition to the harmonic heat flow
AU - Ogawa, Takayoshi
PY - 2003
Y1 - 2003
N2 - 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.
AB - 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.
KW - Bounded mean oscillation
KW - Critical Sobolev inequalities
KW - Harmonic heat flow
KW - Interpolation inequality
KW - Lizorkin-Triebel space
KW - Regularity criterion
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U2 - 10.1137/S0036141001395868
DO - 10.1137/S0036141001395868
M3 - Article
AN - SCOPUS:0242679760
SN - 0036-1410
VL - 34
SP - 1318
EP - 1330
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 6
ER -