On the zero thickness limit of thin ferromagnetic films with surface anisotropy energy

We discuss the behaviour, when the thickness epsilon tends to 0, of thin fe rromagnetic films with surface anisotropy energy. The model equations are g iven by the Landau-Lifshitz equation coupled to Maxweli equations with magn etic polarization. We consider two types of materials: flat and slender cyl inders. Two scalings for the surface anisotropy coefficient are used. In th e first one it is assumed that the coefficient is of order e while in the s econd one we suppose that it is of order 1. We prove global existence of so lutions and show that the zero-thickness limit induces new effects. For exa mple, for slender media we get a nonlocal effect for the magnetic excitatio n while for flat media we obtain a one-dimensional magnetic field.