On the existence and stability of minimizers in ferromagnetic nanowires

We study static 180 degree domain walls in infinite magnetic wires with bounded, C1 and rotationally symmetric cross sections. We prove an existence of global minimizers for the energy of micromagnetics for any bounded C1 cross sections. Under some asymmetry of cross sections we prove a stability result for the minimizers, namely, we show that vectors of micromagnetics having an energy close to the minimal one, must be H1 close to the actual minimizer, which is itself close to the minimizer of the limit energy up to a rotation and a translation.