On the Anisotropic Landau–Lifshitz Equations1

In this paper, we discuss the anisotropic static Landau–Lifshitz equations. We obtain maximum principles and existence results for the small solutions to the Dirichlet problems and the initial-boundary value problems of the corresponding evolution equations. We also construct multiple large smooth solutions in the two dimensions. These problems are dealt with from the viewpoint of harmonic maps with potential.