Lower semicontinuity of quasiconvex integrals

Summary New lower semicontinuity results for quasiconvex integrals. In particular, under certain structure conditions and growth 0≤F(ξ)≤C(∣≤∣ ^q ) the functional ∫ _Ω F(∇u)dx is proved to be lower semicontinuous onW ^1,q with respect to the weak convergence inW ^1,p, p≥q−1. Research supported by the grant No. 201/93/2171 of Czech Grant Agency (GAČR) and by the grant No. 364 of Charles University (GAUK). This article was processed by the author using the Springer-VerlagTex P Jourlg marco package 1991.