Young measure approach to characterization of behaviour of integral functionals on weakly convergent sequences by means of their integrands

It is known that sequential weak lower semicontinuity and weak-strong convergence (in the scalar case) properties of integral functionals may be characterized by means of their integrands. In this paper we introduce a Young measure approach obtaining both these results and the characterization for the second property in the vector-valued case. We discuss also motivations for the definition of strict quasiconvexity, and point out that the characterization of the classes of functionals having weak-strong convergence property everywhere is not a trivial problem in the general case.