Relaxation in ferromagnetism: The rigid case

Summary We undertake the analysis of measure-valued magnetizations in the context of micromagnetics, i.e., parametrized measures coming from sequences of magnetizations, and show that there are no constraints, other than the natural restriction on the support, for this family of probability measures. As a consequence, we prove a general existence theorem for this relaxed formulation and explore relaxation in terms of the first moment of these generalized magnetizations.