Relaxation in magnetostriction

For a family of nonlocal variational problems, a relaxation in terms of You ng measures associated with minimizing sequences is discussed and explicitl y computed. The nonlocality character is the main new feature. These comput ations generalize the same sort of ideas previously used in the analysis of micromagnetics to the case of magnetostriction in which interactions betwe en elastic and magnetic properties are considered. This situation, however, is analyzed under important simplifying assumptions in dimension two.