Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation

We study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to L1 convergence. © 2017 by De Gruyter.