Description
In this talk I will present some recent advances concerning the $C^1$ regularity of minimizers for the vectorial free-discontinuity problem of Griffith. In particular I will try to explain the strategy of proof inspired by the Reifenberg-flat theory, relying on a geometric stopping time argument on the flatness, coupled with a general extension lemma, which was employed in our latest result valid for any dimension $N>2$. This is a recent joint work with C. Labourie, and generalizes, with a different proof, a previous 2 dimensional result obtained in collobaration with J.F. Babadjian and F. Iurlano.
