一类Landau-Lifshitz型泛函的极小元的零点分布

Location of Zero Points of Minimizers in a Landau-Lifshitz Functional

在函数类空间:W={u(x)=(sinf(r)eidθ,cosf(r))∈H1(B,S2);u|аB=g}中研究Landau-Lifshitz型泛函Eε(u,B)=12B∫|u|2dx+1/2ε2 B ∫u23dx的径向极小元uε当ε→0时的极限行为,通过给出uε的整体估计和引入尺度定理,得到了径向极小元uε的第三个分量u3等于1的点的分布状况.

The asymptotic behavior of the radial minimizer uε of the Landau-Lifshitz type functional Eε（u,B）=12 B∫｜аu｜2dx＋12ε2 B∫u23dx when ε→0 in functional space W={u（x）=（sinf（r）eidθ,cosf（r））∈H1（B,S2）;u｜аB=g} was studied.Through the integral estimate of uε and the introduction of Scaling Law,the points where uε3 equals 1 will be located.