Asymptotic behavior of the regularized minimizer of an energy functional in higher dimensions

This paper is concerned with the asymptotic behavior of the regularized minimizer uε = (uε1,uε2, . . . , uεn+1) of an energy functional Eε(u,G) = 1 n G |∇u|n dx + 1 2εn G u2 n+1 dx when ε →0, where G ⊂ Rn is a bounded domain. The author proves W1,n convergence of minimizers to the map un = (u n, 0), where u n is an n-harmonic map. In addition, the author also gives the relation between the zeros of u2ε 1 + u2ε 2 +···+u2 εn and the singularities of u n qualitatively. © 2007 Elsevier Inc. All rights reserved.