Published Paper

Inserted: 1 oct 2025
Last Updated: 7 may 2026

Journal: Comptes Rendus de l'Académie des Sciences
Year: 2025

For convenience, since it is not readily accessible online, De Giorgi’s 1991 paper on free-discontinuity problems is attached to this page.

Abstract:

In this short note, we answer a question raised by E. De Giorgi, showing that a Mumford-Shah minimizer in dimension 2 can admit at most three maximum limit values as approaching the singular set. This result stems from tools developed in the early 2000's by G. David, A. Bonnet, and J.-C. Léger.

Download:

• deGiorgi_John_final.pdf
• degiorgi1991.pdf