Existence of minimizers for the $2$d stationary Griffith fracture model

created by focardi on 09 Mar 2016
modified on 17 Dec 2018

[BibTeX]

Published Paper

Inserted: 9 mar 2016
Last Updated: 17 dec 2018

Journal: C. R. Acad. Sci. Paris, Ser. I
Volume: 354
Number: 11
Pages: 1055--1059
Year: 2016
Doi: 10.1016/j.crma/2016.09.03

Abstract:

We consider the variational formulation of the Griffith fracture model in two spatial dimensions and prove existence of strong minimizers, that is deformation fields which are continuously differentiable outside a closed jump set and which minimize the relevant energy. To this aim, we show that minimizers of the weak formulation of the problem, set in the function space $SBD^2$ and for which 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.