WIAS Preprint No. 1736, (2012)

On the structure of the quasiconvex hull in planar elasticity


  • Heinz, Sebastian

2010 Mathematics Subject Classification

  • 26B25 52A30


  • Quasiconvexity, rank-one convexity, frame invariance




Let K and L be compact sets of real 2x2 matrices with positive determinant. Suppose that both sets are frame invariant, meaning invariant under the left action of the special orthogonal group. Then we give an algebraic characterization for K and L to be incompatible for homogeneous gradient Young measures. This result permits a simplified characterization of the quasiconvex hull and the rank-one convex hull in planar elasticity.

Appeared in

  • Calc. Var. Partial Differ. Equ., 50 (2014) pp. 481--489.

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