Journal of Convex Analysis 18 (2011), No. 1, 037--058
Copyright Heldermann Verlag 2011
On the Characterization of a Class of Laminates for 2 × 2 Symmetric Gradients
Luís Bandeira
CIMA-UE, Dep. de Matemática, Universidade de Évora, Rua Romão Ramalho 59, 7000-671 Évora, Portugal
lmzb@uevora.pt
António Ornelas
CIMA-UE, Dep. de Matemática, Universidade de Évora, Rua Romão Ramalho 59, 7000-671 Évora, Portugal
ornelas@uevora.pt
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.
Keywords: Vector calculus of variations, quasiconvexity, polyconvexity, rank-one convexity, homogeneous gradient Young measure, laminate.
MSC: 49J10; 26B25
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