Lower semicontinuity of certain quasiconvex functionals in Orlicz–Sobolev spaces

Let u:Ω⊂Rn→RNu:Ω⊂Rn→RN be any vector valued function. We prove a semicontinuity result in the weak* topology of Orlicz–Sobolev spaces of the functional F(u,Ω)=∫Ωf(Du(x))dx, where ff is a quasiconvex function satisfying non-standard growth conditions.