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)uε=(uε1,uε2,…,uεn+1) of an energy functionalEε(u,G)=1n∫G|∇u|ndx+12εn∫Gun+12dx when ε→0ε→0, where G⊂RnG⊂Rn is a bounded domain. The author proves W1,nW1,n convergence of minimizers to the map un=(un′,0), where un′ is an n  -harmonic map. In addition, the author also gives the relation between the zeros of uε12+uε22+⋯+uεn2 and the singularities of un′ qualitatively.