Local minimizers for the Ginzburg-Landau energy near critical magnetic field: Part I

We find local minimizers of the two-dimensional Ginzburg-Landau functionals depending on a large parameter k, which describe the behavior of a superco nductor in a prescribed exterior magnetic field h(ex). We prove an estimate on the critical value H-c1 of h(ex)(k), corresponding to the first phase-t ransition in which vortices appear in the superconductor; and we locate the se vortices.