BOUNDARY EFFECTS AND WEAK* LOWER SEMICONTINUITY FOR SIGNED INTEGRAL FUNCTIONALS ON BV

摘要

We characterize lower semicontinuity of integral functionals with respect to weak* convergence in BV, including integrands whose negative part has linear growth. In addition, we allow for sequences without a fixed trace at the boundary. In this case, both the integrand and the shape of the boundary play a key role. This is made precise in our newly found condition - quasi-sublinear growth from below at points of the boundary - which compensates for possible concentration effects generated by the sequence. Our work extends some recent results by Kristensen and Rindler [J. Kristensen and F. Rindler, Arch. Rat. Mech. Anal. 197 (2010) 539-598; J. Kristensen and F. Rindler, Calc. Var. 37 (2010) 29-62].