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).
A density result for GSBD and its application to the approximation of brittle fracture energies
Iurlano F
2014-01-01
Abstract
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).
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