On the Characterization of a Class of Laminates for 2 × 2 Symmetric Gradients

We report on our attempts to disprove the implication from rank-one convexity to quasiconvexity for 2 × 2 symmetric matrices. As a by-product, we have reached a characterization of some laminates, belonging to a special class which we call 3-edge-laminates.