Free Discontinuity Problems

This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.

Contenu
Introduction.- Fine regularity results for Mumford-Shah minimizers: porosity, higher integrability and the Mumford-Shah conjecture.- Variational models for epitaxial growth.- Local and global minimality results for an isoperimetric problem with long-range interactions.