Fine properties of functions with bounded deformation

The paper is concerned with the fine properties of functions u in BD, the space of functions with bounded deformation. We analyse the set of Lebesgue points and the set where these functions have one-sided approximate limits. Moreover, following the analogy with BV, we decompose the symmetric distributional derivative Eu into an absolutely continuous part E(a)u = EuLn, a jump part E(j)u, and a Canter part E(c)u. The main result of the paper is a structure theorem for BD functions, showing that these parts of the derivative can be recovered from the corresponding ones of the one-dimensional sections. Moreover, we prove that BD functions are approximately differentiable in almost every point of their domain.