Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation (Q518933)

The lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation is studied in the paper. The purpose of this work is to extend a result of \textit{G. Bouchitté} et al. [J. Reine Angew. Math. 458, 1--18 (1995; Zbl 0817.49015)] to functionals defined in the space \(BD(\Omega)\) of functions of bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. A suitable class of surface terms is introduced, which makes the functional lower semicontinuous with respect to \(L^1\) convergence.