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Rank-one convexity does not imply quasiconvexity

1992; Cambridge University Press; Volume: 120; Issue: 1-2 Linguagem: Inglês

10.1017/s0308210500015080

1473-7124

Vladimír Šverák,

Analytic and geometric function theory

We consider variational integrals defined for (sufficiently regular) functions u : Ω→ R m . Here Ω is a bounded open subset of R n , Du ( x ) denotes the gradient matrix of u at x and f is a continuous function on the space of all real m × n matrices M m × n . One of the important problems in the calculus of variations is to characterise the functions f for which the integral I is lower semicontinuous. In this connection, the following notions were introduced (see [3], [9], [10]).