On the stability of the Abrikosov lattice in the lowest Landau level

We study the lowest Landau level equation set on simply and doubly-periodic domains (in other words, rectangles and strips with appropriate boundary conditions). To begin with, we study well-posedness and establish the existence of stationary solutions. Then we investigate the linear stability of the lattice solution and prove it is stable for the (hexagonal) Abrikosov lattice, but unstable for rectangular lattices.