Characterization of Generalized Young Measures Generated by Symmetric Gradients

This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical KinderlehrerâPedregal theorem. Our result places such Young measures in duality with symmetric-quasiconvex functions with linear growth. The âlocalâ proof strategy combines blow-up arguments with the singular structure theorem in BD (the analogue of Albertiâs rank-one theorem in BV), which was recently proved by the authors. As an application of our characterization theorem we show how an atomic part in a BD-Young measure can be split off in generating sequences