Density in SBD and approximation of fracture energies

Abstract

. We prove three density theorems, in the strong BD topology, for the three subspaces of SBD functions: SBD ; SBD p ∞ , where the absolutely continuous part of the symmetric gradient is in L p , with p > 1 ; SBD p , whose functions are in SBD p ∞ and the jump set has fi-nite H n − 1 -measure. We compare them with existing results, discussing related approximation of fracture energies.