08-03-2010
Resumo: The relation between quasiconvexity and k-quasiconvexity, k >= 2, is investigated.
It is shown that every smooth strictly k-quasiconvex integrand with p-growth at infinity, p>1, is the restriction to k-th order symmetric tensors of a 1-quasiconvex function with the same growth.
As a consequence, lower semi-continuity results for k-th order variational problems are deduced as corollaries of well known first order theorems.
This generalizes a previous result by Dal Maso, Fonseca, Leoni and Morini, in which the case k=2 was treated.
