Derivation of lower critical magnetic field for anisotropic Ginzburg-Landau model in superconductivity

In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field HC1 which is the first critical value of h ex corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter ., and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers