Existence of minimizers for a variational problem in two-dimensional nonlinear magnetoelasticity

We prove the existence of energy-minimizing configurations for a two-dimens ional, variational model of magnetoelastic materials capable of large defor mations. The model is based on an energy functional which is the sum of the nonlocal self-energy (the energy stored in the magnetic field generated by the body, and permeating the whole ambient space) and of the local anisotr opy energy, which is not weakly lower semicontinuous. A further feature of the model is the presence of a non-convex constraint on one of the unknowns , the magnetization, which is a unit vector field.