Modelling phase transitions via Young measures

We consider the elastic theory of single crystals at constant temperature where the free energy density depends on the local concentration of one or more species of particles in such a way that for a given local concentration vector certain lattice geometries (phases) are preferred. Furthermore we consider possible large deformations of the crystal lattice. After deriving the physical model, we indicate by means of a suitable implicite time discretization an existence result for measure-valued solutions that relies on a new existence theorem for Young measures in infinite settings. This article is an overview of [2]