The Regularity Theory for the Mumford–Shah Functional on the Plane

1. Auflage 2025
ISBN: 978-3-98547-089-1
Verlag: EMS Press

Buch, Englisch, 253 Seiten, Format (B × H): 165 mm x 235 mm, Gewicht: 593 g

Reihe: EMS Monographs in Mathematics

This book provides a thorough and up-to-date account of the state of art of the regularity theory for minimizers of the Mumford–Shah functional of image segmentation in the 2-dimensional setting. Starting with some classical preliminary results, which settle the issue of existence of minimizing couples (u,K), the structure of the set K is then analyzed by using \varepsilon-regularity theorems. Several consequences of the latter are also investigated, in particular leading to different characterizations of the Mumford–Shah conjecture.

The proofs are given with full details, often revisiting the relevant literature and introducing new arguments.

Zielgruppe

Researchers and graduate students interested in the calculus of variations and geometric measure theory.

Autoren/Hrsg.

Lellis, Camillo De

Focardi, Matteo

Über Autor(innen)

Lellis, Camillo De
Institute for Advanced Study, Princeton, USA

Focardi, Matteo
Università degli Studi di Firenze, Italy