Global superheating field for superconductors in a large bounded interval

In continuation of our study of the Ginzburg–Landau equations, we study the asymptotic behavior of the superheating field for a film of width 2d in the regime κ small, κd large, where κ is the Ginzburg–Landau parameter. Using new estimates on the inner magnetic potential, we improve our conditions on the parameter κd and we prove that the local superheating field analyzed in our preceding paper [C. Bolley, F. Foucher, B. Helffer, Superheating field for the Ginzburg–Landau equations in the case of a large bounded interval, J. Math. Phys. 41 (11) (2000) 7263–7289] is a global one. In the regime κ and d large, we also give accurate estimates on the superheating field.