A new approach to Young measure theory relaxation and convergence in energy

Abstract: "The main idea of this paper is to reduce analysis of behavior of integral functionals along weakly convergent sequences to operations with Young measures generated by these sequences. We show that Young measures can be characterized as measurable functions with values in a special compact metric space and that these functions have a spectrum of properties sufficiently broad to realize this idea. These new observations allow us to give simplified proofs of the results of gradient Young measure theory and to use them for deriving the results on relaxation and convergence in energy under optimal assumptions on integrands. In comparison with the first version of this paper, published as a preprint of SISSA, we do not discuss consequences of the new concept of Young measures as measurable functions for the general Young measure theory. However, this time we are more consistent with applications of the new technique to the above questions -- all proofs are now completely based on this technique."