Calculus of Variations and Geometric Measure Theory

G. Dal Maso

Generalised functions of bounded deformation

created by dalmaso on 02 Dec 2011
modified on 18 Nov 2015


Published Paper

Inserted: 2 dec 2011
Last Updated: 18 nov 2015

Journal: J. Eur. Math. Soc. (JEMS)
Volume: 15
Pages: 1943-1997
Year: 2013


We introduce the space GBD of generalized functions of bounded deformation and study the structure properties of these functions: the rectifiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for GBD, which leads to a compactness result for the space GSBD of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to the weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.