Lowest Landau level approach in superconductivity for the Abrikosov lattice close to \(H_{{c}_{2}}\) (Q2474171)

This paper deals with the asymptotic study of the Ginzburg-Landau energy with applied magnetic field \(h_{ex}\). The authors are interested in the regime where \(h_{ex}\) behaves like \(\varepsilon^{-2}\), which characterizes its behavior near the second critical field. This relies on the study of the associated energy functional on a reduced space, which is the first eigenspace for a magnetic operator, also called the lowest Landau level. The analysis is based on refined elliptic estimates combined with a careful asymptotic analysis. Several open problems are also raised in the present paper.