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Variational methods and applications

Regularity of minimizers of the Griffith functional in 2d - (online)

speaker: Antoine Lemenant (Université de Lorraine)

abstract: 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.

timetable:
Tue 7 Sep, 11:30 - 12:20,
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