7 sep 2021 -- 11:30 [open in google calendar]
In this talk I will present some C1 estimates that we have recently obtained on (connected) Griffith minimizers in the planar context with Jean-François Babadjian and Flaviana Iurlano. This functional arises from a variational model of brittle fracture. As it is similar (but much more complicated) than the famous scalar analogue: the Mumford-Shah functional, I will also take the opportunity to rapidly review the classical regularity theory for free-discontinuity problems in order to enlight the encoutered difficulties with the vectorial case. Finally, I will explain how to strengthen the Hausdorff dimension of the singular set, following a work in progress with C. Labourie.