Characterizations of Young measures

Abstract: "The oscillatory properties of a weak convergent sequence of gradients may be decoupled from its deformation properties, a localization property easily shown. Of greater interest is that oscillations may be coupled to a sequence and limit deformation assuming only a kinematic condition and technical condition. This suggests the question of what measures, that is to say, ordinary measures not parametrized measures, may occur as limits of sequences of gradients. We show that they may be characterized by a form of Jensen's inequality for a special class of quasiconvex functions. The consequences of this disparity are of some interest in understanding the sort of approximations, or processes, which lead to complicated microstructures and are relevant to the nature of approximation by Lipshitz functions in general."