Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

S. Conti - M. Focardi - F. Iurlano

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

created by focardi on 09 Mar 2016
modified on 12 Oct 2016


Accepted Paper

Inserted: 9 mar 2016
Last Updated: 12 oct 2016

Journal: C. R. Acad. Sci. Paris, Ser. I
Year: 2016
Doi: 10.1016/j.crma/2016.09.03


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.


Credits | Cookie policy | HTML 5 | CSS 2.1