Truncations under differential constraints and (quasi)convex hulls

In this talk, we discuss the following question: Let us consider a function u in $L^1$ satisfying a differential constraint A u=0 (e.g. A =curl or A = div). Is it possible to modify u slightly, such that it still obeys the differential constraint and is in some better space (i.e. $L^{\infty}$)?

This question can be seen as a generalization of Lipschitz extension/truncation results. I will briefly point out some applications of such a result in the Calculus of Variations.

This talk is based on joint work with L. Behn (Bielefeld) and F. Gmeineder (Konstanz).