ON THE APPROXIMATION OF SBD FUNCTIONS AND SOME APPLICATIONS

Vito Crismale (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

Three density theorems for three suitable subspaces of SBD functions, in the strong BD topology, are proven. The spaces are SBD, SBD p ∞ , where the absolutely continuous part of the symmetric gradient is in L p , with p > 1, and SBD p , whose functions are in SBD p ∞ and the jump set has finite H n−1-measure. This generalises on the one hand the density result [12] by Chambolle and, on the other hand, extends in some sense the three approximation theorems in [27] by De Philippis, Fusco, Pratelli for SBV , SBV p ∞ , SBV p spaces, obtaining also more regularity for the absolutely continuous part of the approximating functions. As application, the sharp version of two Γ-convergence results for energies defined on SBD 2 is derived.

Domaines: Mathématiques [math]; Analyse fonctionnelle [math.FA]

Vito Crismale. ON THE APPROXIMATION OF SBD FUNCTIONS AND SOME APPLICATIONS. 2018. ⟨hal-01811177⟩