The regularity theory for the Mumford-Shah functional on the plane / Camillo De Lellis, Matteo Focardi.

Format:

Book

Author/Creator:

De Lellis, Camillo, author.

Focardi, Matteo, author.

Series:

EMS monographs in mathematics

Language:

English

Subjects (All):

Calculus of variations.

Mathematical optimization.

Physical Description:

x, 256 pages : illustrations ; 25 cm

Place of Publication:

Berlin : EMS Press, [2025]

Summary:

"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 , the structure of the set is then analyzed by using -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." - publisher

Contents:

Introduction

Density bounds, compactness, variations, and monotonicity

Pure jumps and triple junctions

The Bonnet-David rigidity theorem for cracktips

Epsilon regularity of the cracktip

Some consequences of the epsilon-regularity theory.

Notes:

Includes bibliographical references (pages 249-251) and index.

Other Format:

e-book version

ISBN:

9783985470891

3985470898

OCLC:

1525720343

Publisher Number:

9783985470891