Limiting behavior of minimizers of P(x)-Ginzburg-Landau type

Abstract

This paper is concerned with the asymptotic behavior of the radial minimizers of the p(x)-Ginzburg-Landau type functional. We prove the  uniqueness of radial minimizers in the case of 1 < p(x) < 2. In addition, this unique minimizer can be viewed as a limit of radial minimizers of a  regularized functional. Based on these results, we obtain the Holder convergence by establishing the local W1;l-estimate. A new technique of counteracting the  singularity plays a key role by estimating an accurate asymptotic rate. We believe that such a uniform estimate can provide some enlightenments how  to handle other Ginzburg-Landau type equations, such as the p(x)-Laplace sy tem without the radial structure.