Orateur
Description
The Griffith functional, arising in variational models of crack propagation and linearized elasticity, shares many features with the classical Mumford–Shah functional. A major difficulty in this vectorial setting is that the energy only controls the symmetric part of the gradient, rather than the full gradient itself. In this talk, I will present a strategy to obtain the L^2-integrability of the full gradient of two-dimensional Griffith minimizers through local Korn-type inequalities. This is part of a recent joint work with Camille Labourie and Lorenzo Lamberti (Université de Lorraine, Nancy). Along the way, and because this is how the story behind this work began, we will briefly discuss a conjecture formulated by E. De Giorgi in 1991 on the behavior of Mumford–Shah minimizers near their singular set. In dimension two, this question can be addressed using tools developed by G. David, A. Bonnet, and J.-C. Léger, and I will explain how these ideas naturally lead to the Griffith setting.