A density result for GSBD and its application to the approximation of brittle fracture energies

We present an approximation result for functions belonging to the space with square integrable and finite. The approximating functions are piecewise continuous functions such that in , in , , and . As an application, we provide the extension to the vector-valued case of the -convergence result in proved by Ambrosio and Tortorelli (Commun Pure Appl Math 43:999-1036, 1990; Boll. Un. Mat. Ital. B (7) 6:105-123, 1992).