Boundary regularity for minimizers of the micromagnetic energy functional

Details Boundary regularity for minimizers of the micromagnetic energy functional Boundary regularity for minimizers of the micromagnetic energy functional

2010-06-24

arxiv.org/abs/1006.4766v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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