We introduce the space of generalized functions of bounded deformation and study the structure properties of these functions: the rectiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for , which leads to a compactness result for the space of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.
Cite this article
Gianni Dal Maso, Generalised functions of bounded deformation. J. Eur. Math. Soc. 15 (2013), no. 5, pp. 1943–1997DOI 10.4171/JEMS/410