Estimates for convergence rate of an n-Ginzburg-Landau type minimizer

Abstract

The paper is concerned with the asymptotic analysis of a minimizer of an $n$-Ginzburg-Landau type functional. The convergence rate of the module of minimizers is presented when the parameter $\varepsilon$ goes to zero. This conclusion shows that the functional converges to $\frac{1}{n}\int|\nabla u_n|^n$ locally when $\varepsilon \to 0$, where $u_n$ is an $n$-harmonic map.