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

Antonin Chambolle (1) , Sergio Conti (2) , Flaviana Iurlano (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Instutute for Applied Mathematics [Bonn]
3 LJLL - Laboratoire Jacques-Louis Lions

We prove that special functions of bounded deformation with small jump set are 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 Leaci to the linearized context in dimension n and to establish the closedness of the jump set for local minimizers of the Griffith energy.

Mots clés: Brittle fracture; functions with bounded deformation; free discontinuity problems; strong solutions

Domaines: Analyse fonctionnelle [math.FA]; Mécanique des solides [physics.class-ph]

Antonin Chambolle, Sergio Conti, Flaviana Iurlano. Approximation of functions with small jump sets and existence of strong minimizers of Griffith's energy. 2017. ⟨hal-01610691v1⟩