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