  We show general lower semicontinuity and relaxation theorems for
linear-growth integral functionals defined on vector measures that satisfy
linear PDE side constraints (of arbitrary order). These results generalize
several known lower semicontinuity and relaxation theorems for BV, BD, and for
more general first-order linear PDE side constrains. Our proofs are based on
recent progress in the understanding of singularities of measure solutions to
linear PDEs and of the generalized convexity notions corresponding to these PDE
constraints.
