The author proves the Wi,p convergence of the radial minimizers uE = (uE1, uE2, uE3) of an energy function as EPSILON goes to 0, and the zeros of the uE1 2 + uE22 are located roughly. In addition, the estimates of the convergent rate of uE3 2 are presented.
Yutian Lei. "Asymptotic Analysis of the Radial Minimizers of an Energy Functional." Methods Appl. Anal. 10 (1) 067 - 080, March 2003.