Abstract
In this paper, we discuss the vortex structure of the superconducting thin films placed in a magnetic field. The discussion is based on a system of simplified Ginzburg--Landau equations. We obtain the estimate for the lower critical magnetic field Hc1 , in the sense that it is the first critical value of hex, the applied field, for which the minimal energy among vortexless configurations is equal to the minimal energy among single-vortex configurations; moreover, it corresponds to the first phase transition in which vortices appear in the superconductor. We also discuss the location of these vortices and the asymptotic behavior of the local minimizers.
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