Abstract
The variational theory of brittle fracture of elastic materials (Frankfurt-Marigo, 1998) is based on the minimization of a so-called " de Griffith " energy (inspired by Mumford-Shah in image processing) which couples a linearized elasticity energy term and the length or surface of the fracture zone. We will recall how to obtain " Poincaré-Korn " or " Korn " type estimates in the associated energy space (defined only around 2010 by Dal Maso) and how we can deduce compactness results, and the existence of weak and strong minimizers for the energy. This is based on collaborative work with F. Cagnetti (Bath), S. Conti (Bonn), V. Crismale (Rome), G. Francfort (Paris), F. Iurlano (Paris), L. Scardia (Edinburgh).
