  We study static 180 degree domain walls in infinite magnetic wires with
bounded, $C^1$ and rotationally symmetric cross sections. We prove an existence
of global minimizers for the energy of micromagnetics for any bounded $C^1$
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 $H^1$ close to a minimizer
of the limiting energy up to a rotation and a translation.

Analysis of PDEs