Bounded deformation vs bounded variation

Example 7.7 in

L. Ambrosio, A. Coscia, Alessandra, G. Dal Maso, Fine properties of functions with bounded deformation. Arch. Rational Mech. Anal. 139 (1997), no. 3, 201–238.

This paper discusses counterexamples to Korn's inequality in $L^1$ spaces: https://www.mis.mpg.de/preprints/2003/preprint2003_93.pdf