Relaxation results for a class of variational integrals (Q1066073)

Relaxation results for the functional \(F(u,G)=\int_{G}f(u,Du)dx\), where f(s,z) is not necessarily continuous with respect to s, are given. The authors obtain an integral representation formula for the greatest functional \(\bar F(\)u,G) which is lower semicontinuous with respect to the \(L^ 1_{loc}(G)\)-topology and less than or equal to F(u,G). They also give an explicit way to construct the integrand function in \(\bar F.\)