TY - JOUR
T1 - Higher order quasiconvexity reduces to quasiconvexity
JF - Arch. Ration. Mech. Anal. 171 (2004) 55-81
Y1 - 2004
A1 - Gianni Dal Maso
A1 - Irene Fonseca
A1 - Giovanni Leoni
A1 - Massimiliano Morini
AB - 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.
PB - Springer
UR - http://hdl.handle.net/1963/2911
U1 - 1789
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -