In this paper it is shown that higher-order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower-semicontinuity results for second-order variational problems are deduced as corollaries of well-known first-order theorems.
Higher-order quasiconvexity reduces to quasiconvexity / G. Dal Maso; I. Fonseca; G. Leoni; M. Morini. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 171(2004), pp. 55-81. [10.1007/s00205-003-0278-1]