Maximum principles, uniqueness and existence for harmonic maps with potential and Landau-Lifshitz equations

In this paper, we consider the harmonic maps with potential from compact Riemannian manifold with boundary into a convex ball in any Riemannian manifold. We will establish some general properties such as the maximum principles, uniqueness and existence for these maps, and as an application of them, we derive existence and uniqueness result for the Dirichlet problem of the Landau-Lifshitz equations. Received: December 10, 1997 / Accepted: June 29, 1998