GAUGE UNIQUENESS OF SOLUTIONS TO THE GINZBURG-LANDAU SYSTEM FOR SMALL SUPERCONDUCTING DOMAINS

摘要

We study the Ginzburg-Landau system with an applied magnetic field for two-dimensional domains. For small bounded, smooth, and simply connected domains, we show that superconducting solutions are unique up to a gauge and that for this geometry, materials exhibit no hysteresis effects and no vortex nucleation for any kappa.