Every GBD function carries a symmetric-matrix-valued measure whose decomposition separates absolutely continuous, Cantor, and jump contributions, and GSBD is exactly the class where the Cantor part vanishes.
A characterization of Generalized functions of Bounded Deformation
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We show that Dal Maso's GBD space, introduced for tackling crack growth in linearized elasticity, can be defined by simple conditions in a finite number of directions of slicing.
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A matrix-valued measure associated to the derivatives of a function of generalised bounded deformation
Every GBD function carries a symmetric-matrix-valued measure whose decomposition separates absolutely continuous, Cantor, and jump contributions, and GSBD is exactly the class where the Cantor part vanishes.