Existence, regularity and local uniqueness of the solutions to the Maxwell–Landau–Lifshitz system in three dimensions

We study a model of ferromagnetism governed by Maxwell's equations coupled with the non-linear Landau–Lifshitz equation of micromagnetism. We are interested in the cases of space-periodic solutions for 3D domains. Obtaining the regularity of the solution m in space and of the solutions E, H in space we state the existence theorem. Finally, we prove the local uniqueness of the solutions.