A dual approach to regularity in thin film micromagnetics - Melcher, C (2007)
We prove a regularity result in the two-dimensional theory of soft ferromagnetic films. The associated Euler-Lagrange equation is given by a nonlocal degenerate variational inequality involving fractional derivatives. A difference quotient type argument based on a dual formulation in terms of magnetostatic potentials yields a Hölder estimate for the uniquely determined gradient projection of the magnetization field. © Springer-Verlag 2007.