Abstract :

We study the asymptotic limit of solutions of the Ginzburg-Landau system describing a superconductor in an applied magnetic field, in the ``London limit'' of a Ginzburg-Landau parameter $\kappa$ tending to infinity. We examine the asymptotic behavior of the ``vorticity-measures'' associated to the vortices of the solution, and prove that passing to the limit in the equations (via the ``stress-energy tensor'') yields a criticality condition on the limiting measures. This condition allows to describe the possible locations and densities of the vortices.