Which special functions of bounded deformation have bounded variation

摘要: Functions of bounded deformation (BD) arise naturally in the study fracture and damage a geometrically linear context. They are related to functions variation (BV), but less well understood. We discuss here relation BV under additional regularity assumptions, which may require regular part strain have higher integrability or jump set finite area Cantor vanish. On positive side, we prove that BD piecewise affine on Caccioppoli partition GSBV, SBD p approximately continuous -almost everywhere away from set. negative construct function is not has distributional consisting only part, one part.