This title presents the reader with a systematic introduction to a class of variational problems called 'free discontinuity problems'. The book bridges the gap between the research level and elementary courses on measure theory and calculus of variation at a level suitable for graduate students. Series: Oxford Mathematical Monographs. Num Pages: 452 pages, 2 halftones, 25 line figures. BIC Classification: PBKF; PBKQ; PBW. Category: (P) Professional & Vocational. Dimension: 241 x 162 x 37. Weight in Grams: 776. . 2000. Hardback. . . . .

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Bibliographic Details

Title: Functions of Bounded Variation and Free Discontinuity Problems
Publisher: Oxford University Press
Publication Date: 2000
Language: English
ISBN 10: 0198502451
ISBN 13: 9780198502456
Binding: Hardcover
Condition: New

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.

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