Tutorial on quasiconvexity and regularity of minimizers

In this expository lecture I will explain how to show partial regularity of minimizing mappings for both convex and quasiconvex energy integrands. The technique is to linearize by ``blowing up'' and the basic issue is establishing compactness of a rescaled sequence of functions.
I will discuss also how to modify these ideas in a case that we have a determinant constraint.