  Lower semicontinuity of surface energies in integral form is known to be
equivalent to BV-ellipticity of the surface density. In this paper, we prove
that BV-ellipticity coincides with the simpler notion of biconvexity for a
class of densities that depend only on the jump height and jump normal, and are
positively 1-homogeneous in the first argument. The second main result is the
analogous statement in the setting of bounded deformations, where we show that
BD-ellipticity reduces to symmetric biconvexity. Our techniques are primarily
inspired by constructions from the analysis of structured deformations and the
general theory of free discontinuity problems.
