Higher order regularity results in 3D for the Landau–Lifshitz equation with an exchange field

We derive and prove higher order regularity results for the Landau–Lifshitz (LL) equation describing the evolution of spin fields in continuum ferromagnets. These results are based on the weight κ(s)={min1,s}κ(s)={min1,s} which helps to get nonlinear parts under control.