  A model problem of magneto-elastic body is considered. Specifically, the case
of a two dimensional circular disk is studied. The functional which represents
the magneto-elastic energy is introduced. Then, the minimisation problem,
referring to the simplified two-dimensional model under investigation, is
analysed. The existence of a minimiser is proved and its dependence on the
eigenvalues of the problem is investigated. A bifurcation result is obtained
corresponding to special values of the parameters.
