Gradient young measures and applications to optimal design

We briefly review the relevance of gradient Young measures in vector variational problems, especially when these are not convex. In particular, their relationship to weak lower semicontinuity and relaxation is highlighted. We also describe how some of these ideas can be used to examine optimal design problems in conductivity. This turns out to be another interesting training ground for the typical techniques of non-convex, vector variational problems that have been so successful in the context of hyperelasticity.