Abstract: In this dissertation, Asymptotic behavior of the radial minimizer uε of the Landau－Lifshitz function Eε(u, B)＝u2dx+udx , in W＝｛u(x)＝[sin f(r)eidθ, cosf(r)]∈H1(B,S2); u｜?坠B＝g｝; u｜?坠B＝g｝ has been studied. And several estimates of the convergence rate of u to 0 have been proposed by establishing the local convergence of the radial minimizer uε in the H1 sense.

Key words: radial minimizer, symptotic behavior, Landau－Lifshitz functions