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

Representation of Weak Limits and Definition of Nonconservative Products

“…Related issues appear in studies of transport equations with discontinuous coefficients (e.g., LeFloch [15,16], LeFloch and Xin [20], Poupaud and Rascle [22], Bouchut and James [4]) and in minimization of certain types of functionals in the space of functions of bounded variation (e.g., Aviles and Giga [1], Raymond and Seghir [26]). The reader is referred to Colombeau [6], Colombeau and Leroux [7] for a theory of nonconservative products in a weaker functional framework.…”