  The goal of this paper is to describe the oscillatory microstructure that can
emerge from minimizing sequences for nonconvex energies. We consider integral
functionals that are defined on real valued (scalar) functions $u(x)$ which are
nonconvex in the gradient $\nabla u$ and possibly also in $u$. To characterize
the microstructures for these nonconvex energies, we minimize the associated
relaxed energy using two novel approaches: i) a semi-analytical method based on
control systems theory, ii) and a numerical scheme that combines convex
splitting together with a modified version of the split Bregman algorithm.
These solutions are then used to gain information about minimizing sequences of
the original problem and the spatial distribution of microstructure.
