Existence of minimizers for the 2d stationary Griffith fracture model
Sergio Conti, Matteo Focardi, Flaviana Iurlano · Comptes Rendus Mathématique · 2016
We consider the variational formulation of the Griffith fracture model in two spatial dimensions and prove the existence of strong minimizers, that is deformation fields that are continuously differentiable outside a closed jump set and that minimize the relevant energy. To this aim, we show that minimizers of the weak formulation of the problem, set in the function space G S B D 2 and whose existence is well known, are actually strong minimizers following the approach developed by De Giorgi, Carriero, and Leaci in the corresponding scalar setting of the Mumford–Shah problem.