A rigorous treatment of nucleation modes spectrum in micromagnetics

The nucleation problem for an anisotropic ellipsoidal magnetic particle is studied in the framework of micromagnetics. The stability of a spatially uniform micromagnetic equilibrium is connected to the positive definitiveness of a quadratic functional which is associated to an appropriate self-adjoint integro-differential operator. The spectrum of this operator is studied rigorously by using the theory of continuous and weakly coercive bilinear forms.