  We consider nontrivial finite energy traveling waves for the Landau-Lifshitz
equation with easy-plane anisotropy. Our main result is the existence of a
minimal energy for these traveling waves, in dimensions two, three and four.
The proof relies on a priori estimates related with the theory of harmonic maps
and the connection of the Landau-Lifshitz equation with the kernels appearing
in the Gross-Pitaevskii equation.
