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We prove that special functions of bounded deformation with small jump setare close in energy to functions which are smooth in a slightly smaller domain.This permits to generalize the decay estimate by De Giorgi, Carriero, and Leacito the linearized context in dimension n and to establish the closedness of thejump set for local minimizers of the Griffith energy.

Approximation of functions with small jump sets and existence of strong minimizers of Griffith's energy