On the Ginzburg-Landau model of a superconducting ball in a uniform field

We consider the three-dimensional Ginzburg-Landau model for a solid spherical superconductor in a uniform magnetic field, in the limit as the Ginzburg-Landau parameter K = 1/epsilon -> infinity. By studying a limiting functional we identify a candidate for the lower critical field H-C1, the value of the applied field strength at which minimizers first exhibit vortices. For applied fields of this strength we show the existence of locally minimizing solutions with vortices located along a diameter of the sphere parallel to the applied field direction. To analyze these problems we use a combination of techniques, involving least perimeter problems, weak Jacobians and rectifiable currents, and special Hodge decompositions. (c) 2005 Elsevier SAS. All rights reserved.