Lower semicontinuity and relaxation of signed functionals with linear growth in the context of A-quasiconvexity

摘要

A lower semicontinuity and relaxation result with respect to weak-* convergence of measures is derived for functionals of the form, where admissible sequences {μ_n} are such that {Aμ_n} converges to zero strongly in W~(-1,q) _(loc)(Ω) and A is a partial differential operator with constant rank. The integrand f has linear growth and L~∞-bounds from below are not assumed.