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

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. Journal de Mathématiques Pures et Appliquées, 2019, 128 (9), pp.119--139. ⟨10.1016/j.matpur.2019.02.001⟩. ⟨hal-01610691v2⟩