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- ItemOn the structure of the quasiconvex hull in planar elasticity(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Heinz, SebastianLet 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.
- ItemQuasiconvexity equals rank-one convexity for isotropic sets of 2 x 2 matrices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Heinz, SebastianLet K be a given compact set of real 2x2 matrices that is isotropic, meaning invariant under the left and right action of the special orthogonal group. Then we show that the quasiconvex hull of K coincides with the rank-one convex hull (and even with the lamination convex hull of order 2). In particular, there is no difference between quasiconvexity and rank-one convexity for K. This is a generalization of a known result for connected sets.