  Motivated by the construction of time-periodic solutions for the
three-dimensional Landau-Lifshitz-Gilbert equation in the case of soft and
small ferromagnetic particles, we investigate the regularity properties of
minimizers of the micromagnetic energy functional at the boundary. In
particular, we show that minimizers are regular provided the volume of the
particle is sufficiently small. The approach uses a reflection construction at
the boundary and an adaption of the well-known regularity theory for minimizing
harmonic maps into spheres.
