On the Energy of Type - II

We study the Ginzburg-Landau energy of superconductors with high , put in a prescribed external eld h ex , for h ex varying between the two critical elds H c 1 and H c 2. As ! +1, we give the leading term in the asymptotic expansion of the minimal energy and show that energy minimizers have vortices whose density tends to be uniform and equal to h ex. In this paper, we study minimizers of the Ginzburg-Landau functional J(u; A) = 1 2 Z jr A uj 2 + jh ? h ex j 2 + 2 2 ? 1 ? juj 2 2 dx; that corresponds to the free energy of a superconductor in a prescribed, constant magnetic eld h ex. Here, R 2 is the smooth, bounded and connected section of the super-conductor (supposed to be cylindrical); and the unknowns are the complex-valued order 1