Some evidence in favor of Morrey's conjecture
  We provide further evidence to favor the fact that rank-one convexity does not imply quasiconvexity for two-component maps in dimension two. We provide an explicit family of maps parametrized by $\tau$, and argue that, for small $\tau$, they cannot be achievable by lamination. In this way, Morrey's conjecture might turn out to be correct in all cases. 
Pablo Pedregal
math.OC