Minimization of a quasi-linear Ginzburg–Landau type energy

Let GG be a smooth bounded domain in R2R2. Consider the functional Eε(u)=12∫G(p0+t|x|k|u|l)|∇u|2+14ε2∫G(1−|u|2)2 on the set Hg1(G,C)={u∈H1(G,C);u=g on ∂G} where gg is a given boundary data with degree d≥0d≥0. In this paper we will study the behavior of minimizers uεuε of EεEε and we will estimate the energy Eε(uε)Eε(uε).