Functions of Bounded Variation and Free Discontinuity Problems (Oxford Mathematical Monographs)

Ambrosio, Luigi,Fusco, Nicola,Pallara, Diego

ISBN 10: 0198502451 / ISBN 13: 9780198502456

Published by Oxford University Press, 2000

About this Item

Seller Inventory # mon0003681453

Bibliographic Details

• Title: Functions of Bounded Variation and Free Discontinuity Problems (Oxford Mathematical Monographs)
• Publisher: Oxford University Press
• Publication Date: 2000
• Language: English
• ISBN 10: 0198502451
• ISBN 13: 9780198502456
• Binding: hardcover
• Condition: Very Good

About this title

Synopsis

This book deals with a class of mathematical problems which involve the minimization of the sum of a volume and a surface energy and have lately been referred to as 'free discontinuity problems'. The aim of this book is twofold: The first three chapters present all the basic prerequisites for the treatment of free discontinuity and other variational problems in a systematic, general, and self-contained way. In the later chapters, the reader is introduced to the theory of free discontinuity problems, to the space of special functions of bounded variation, and is presented with a detailed analysis of the Mumford-Shah image segmentation problem. Existence, regularity and qualitative properties of solutions are explained and a survey is given on the current knowledge of this challenging mathematical problem. The theory embodies classical problems, e.g. related to phase transitions, or fracture and plasticity in continuum mechanics, as well as more recent ones like edge detection in image analysis. This book provides the reader with a solid introduction to the field, written by principle contributors to the theory.

About the Author

Luigi Ambrosio is at Scuola Normale Superiore, Pisa. Nicola Fusco is in the Department of Mathematics, Universita di Firenze.