NCSU Differential Equations/Nonlinear Analysis Seminars

Location and Time: SAS 4201, Wednesday 15:00 -16:00

Organizers: Lorena Bociu, Patrick Combettes, Ryan Murray, and Khai T. Nguyen

NEXT TALK

Wednesday, April 08, 15:00-16:00, Zoom: Link

Speaker: Antoine Lemenant, IECL: Institut Elie Cartan de Lorraine, France
Title: On a conjecture of E. De Giorgi for free discontinuity problems
Abstract: In a 1991 paper, E. De Giorgi formulated a series of nine conjectures concerning the now well-known Mumford–Shah functional, some of which remain open to this day. Among them, Conjecture 2 states that, in dimension N, the number of possible limit values of a minimizer as approaching its singular set should be less than or equal to N+1. In this talk, I will describe how to give a positive answer to this question in dimension 2, using tools developed by G. David, A. Bonnet, and J.-C. Léger in the 2000s. This work is part of a recent collaboration with Camille Labourie (Université de Lorraine, Nancy). We will then discuss to what extent this result can be (partially) extended to the Griffith functional, which arises in models of crack propagation and motivates ongoing work in collaboration with Camille Labourie and Lorenzo Lamberti (both at Université de Lorraine, Nancy).
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