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

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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. https://doi.org/10.68381/jca18002

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press.