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

Luís Bandeira; António Ornelas

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

Vector calculus of variations
quasiconvexity
polyconvexity
rank-one convexity
homogeneous gradient Young measure
laminate

Mathematics Subject Classification

49J10; 26B25

Suggested citation

L. Bandeira, A. Ornelas. “On the Characterization of a Class of Laminates for 2 × 2 Symmetric Gradients.” Journal of Convex Analysis 18 (2011), No. 1, 37–58.