This talk first introduces generalized Young measures (or DiPerna/Majda measures) in an $L^1$-setting. This extension to classical Young measures is able to quantitatively account for both oscillation and concentration phenomena in generating sequences.
We establish several fundamental properties like compactness and representation of nonlinear integral functionals and present some examples. Then, generalized Young measures generated by $W^{1,1}$- and $BV$-gradients are more closely examined and several tools to manipulate them (including averaging and approximation) are presented.
Finally, we address the question of characterizing the set of generalized Young measures generated by gradients in the spirit of the Kinderlehrer-Pedregal Theorem.
This is joint work with Jan Kristensen.