一类Landau-Lifshitz型泛函的极小元的H_（loc）~1收敛性

The H_（loc）~1 convergence of minimal element of a Landau-Lifshitz type functional

在函数类空间:W={u(x)=(sinf(r)eidθ,cosf(r))∈H1(B,S2);μ|B=g}中研究Landau-Lifshitz型泛函 Eε(u,B)=1/2∫B|▽μ|2dx+(1/2ε2)∫Buμ32dx的径向极小元uε,通过引入辅助泛函和选取光滑切断因子的方法研究其Hl1oc收敛性。

In the expanse of functions category：the research,which is based on the method of introduction of auxiliary functional and selecting smooth cutting factor,on the H_（loc）~1 convergence of μe is introduced in this paper.And the μe is the radial minimizer of a Landau-Lifshitz type functional Eε（u,B）=1/2∫B｜▽μ｜2dx＋（1/2ε2）∫Buμ32dx,the domain of which is W={u（x）=（sinf（r）eidθ,cosf（r））∈H1（B,S2）;μ｜B=g}