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

A Modified Split Bregman Algorithm for Computing Microstructures Through Young Measures