Abstract: The relation between quasiconvexity and -quasiconvexity, , is investigated. It is shown that every smooth strictly -quasiconvex integrand with -growth at infinity, , is the restriction to -th order symmetric tensors of a quasiconvex function with the same growth. When the smoothness condition is dropped, it is possible to prove an approximation result. As a consequence, lower semicontinuity results for -th order variational problems are deduced as corollaries of well-known first order theorems. This generalizes a previous work by Dal Maso, Fonseca, Leoni and Morini, in which the case was treated.

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