  We report first-principles calculations, within the density functional
theory, on the structural and energetic properties of 180$^\circ$ stripe
domains in (PbTiO$_{3}$)$_{n}$/(SrTiO$_{3}$)$_{n}$ superlattices. For the
explored periodicities ($n$=3 and 6) we find that the polydomain structures
compete in energy with the monodomain phases. Our results suggest the
progressive transition, as a function of $n$, from a strong to a weak
electrostatic coupling regime between the SrTiO$_{3}$ and PbTiO$_{3}$ layers.
Structurally, they display continuous rotation of polarization connecting
180$^\circ$ domains. A large offset between [100] atomic rows across the domain
wall and huge strain gradients are observed. The domain wall energy is very
isotropic, depending very weakly on the stripe orientation.
