We prove a general criterion for the lower semicontinuity of Burkill-Cesari integral in abstract setting. The basic idea, which is inspired by a classical Menger's conjecture, consists on reducing this result to a suitable adaptation of the semicontinuity of the length of a curve. Some noteworthy applications to the Weierstrass functionals of the Calculus of Variations in BV setting are also presented.
展开▼
