Lower semicontinuity for quasiconvex integrals of higher order

Abstract.

We consider a functional of the type ${\cal F}(u) = \int_\Omega F(x,u,\ldots,{D^k}u)dx$, where $\Omega$ is an open bounded set of ${\Bbb R}^n$ and F is a Carathéodory function. By an approximation argument we prove the lower semincontinuity of $\cal F$ with respect to the weak topology of $W^{k,p} (\Omega; {\Bbb R}^m)$ under p-growth conditions for the integrand F.