Lower Semicontinuity and Integral Representation of Functionals in BV([a, b]; Rm)

We obtain new lower semicontinuity results for an integral functional on the space BV([a, b]; Rm) endowed with its weak-star topology. We also prove, under some estimates on the integrand of the functional, that this functional is the lower semicontinuous regularization (in BV([a, b]; Rm)-weak*) of a classical functional defined on W1,1(a, b; R(m)).