On the energy of type-II superconductors in the mixed phase

We study the Ginzburg-Landau energy of superconductors with high kappa, put in a prescribed external field h(ex), for h(ex) varying between the two cr itical fields H-c1 and H-c3. As kappa --> +infinity, we give the leading te rm in the asymptotic expansion of the minimal energy and show that energy m inimizers have vortices whose density tends to be uniform and equal to h(ex ).