THE GLOBAL MINIMIZERS OF ANISOTROPIC GINZBURG-LANDAU MODEL IN SUPERCONDUCTIVITY

The existence of the global minimizers of the Ginzburg-Landau functional for an anisotropic superconducting sample in a magnetic field $h_{ex}$ below the first critical field $H_{C_{1}}$ is proved. It is shown that there exists a vortex-less solution coincide with the solution found by the authors in a related paper, and that the density of the vortices is relevant to the applied field as $H_{c_{1}}h_{ex}H_{c_{2}}$.