Bulk superconductivity in Type II superconductors near the second   critical field
  We consider superconductors of Type II near the transition from the 'bulk superconducting' to the 'surface superconducting' state. We prove a new $L^{\infty}$ estimate on the order parameter in the bulk, i.e. away from the boundary. This solves an open problem posed by Aftalion and Serfaty. 
S. Fournais and B. Helffer