Bibliography

(eng): We state necessary and sufficient conditions for weak lower semicontinuity of integral functionals of the form u bar right arrow integral(Omega) h(x, u(x)) dx, where h is continuous and possesses a positively p-homogeneous recession function, p > 1, and u is an element of L-p(Omega, R-m) lives in the kernel of a constant-rank first-order differential operator A which admits an extension property. In the special case A = curl, apart from the quasiconvexity of the integrand, the recession function's quasiconvexity at the boundary in the sense of Ball and Marsden is known to play a crucial role. Our newly defined notions of A-quasiconvexity at the boundary, generalize this result. Moreover, we give an equivalent condition for the weak lower semicontinuity of the above functional along sequences weakly converging in L-p(Omega, R-m) and approaching the kernel of A even if A does not have the extension property.