Weak convergence of integrands and the Young measure representation

Abstract: "Validity of the Young measure representation is useful in the study of microstructure of ordered solids. Such a Young measure, generated by a minimizing sequence of gradients converging weakly in LP, often needs to be evaluated on functions of p[superscript th] power polynomial growth. We give a sufficient condition for this in terms of the variational principle. The principal result concerns lower semicontinuity of functionals integrated over arbitrary sets, Theorem 1.2. The question arose in the numerical analysis of configurations. Several applications are given. Of particular note, Young measure solutions of an evolution problem are found.