Asymptotics for the Ginzburg–Landau Equation in Arbitrary Dimensions

Let Ω be a bounded, simply connected, regular domain of RN, N⩾2. For 0<ε<1, let uε: Ω→C be a smooth solution of the Ginzburg–Landau equation in Ω with Dirichlet boundary condition gε, i.e.,[formula] We are interested in the asymptotic behavior of uε as ε goes to zero under the assumption that Eε(uε)⩽M0 |log ε| and some conditions on gε which allow singularities of dimension N−3 on ∂Ω.