Magneto-elasticity on the disk

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.