Asymptotic behavior for minimizers of a p-energy functional associated with p-harmonic map

with a small parameter ε > 0 was introduced in the study of some simplified model of high-energy physics, which controls the statics of planner ferromagnets and antiferromagnets (see [9] and [12]). The asymptotic behavior of minimizers of Eε(u) had been studied by Fengbo Hang and Fanghua Lin in [7]. When the term u 3 2ε replaced by (1−|u|) 4ε and S 2 replaced by R, the problem becomes the simplified model of the Ginzburg-Landau theory for superconductors and was well studied in many papers such as [1][2] and [13]. These works show that the properties of harmonic map with S-value can be studied via researching the minimizers of the functional with some penalization terms. Indeed, Y.Chen and M.Struwe used the penalty method to establish the global existence of partial regular weak solutions of the harmonic map flow (see [4] and [6]). M.Misawa studied the p-harmonic maps by using the same idea of the penalty method in