Abstract

The Ginzburg-Landau functional
$$J(u,A)=\frac{1}{2}\int_{\Omega} |\nabla_A u|^2 + |h-h_{ex}|^2 + \frac{1}{2\epsilon^2} (1-|u|^2)^2,$$
is the energy of a superconductor submitted to a magnetic field $h_{ex}$. The main feature is the apparition of
vortices for certain values of the applied field. After the work of Bethuel- Brezis- Helein on a simplified energy
(without magnetic field), we (partly joint work with E. Sandier) have studied this full functional in the asymptotics
of  small $\,\epsilon$, and  developed a similar analysis for  it. We have  particularly focused  on describing the
energy - minimizing configurations, their vortices, and determining a mean-vorticity measure.