Functions of Bounded Variation and Free Discontinuity Problems
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Functions of Bounded Variation and Free Discontinuity Problems Description
This book presents the reader with a systematic introduction to a class of variational problems called 'free discontinuity problems'. Examples of such problems come, for instance, from fracture mechanics, image analysis, or the theory of phase transitions. 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. The first half of the book contains a comprehensiveand updated treatment of the theory of Functions of Bounded Variation and of the mathematical prerequisites of that theory, that is Abstract Measure Theory and Geometric Measure Theory.
Details
| OPC | PDHSNZS |
|---|---|
| Codes | 0198502451 (ISBN-10) |
| 9780198502456 (ISBN) |
Disclaimer: The information below is provided by various external sources and should be used as a guide only.
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 refered 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. Free discontinuity problems reveal a wide range of applications. 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. The first half of the book contains a comprehensive and updated treatment of the theory of Functions of Bounded Variation and of the mathematical prerequisites of that theory that is Abstract Measure Theory and Geometric Measure Theory.
Alternative names:
- ISBN Functions of Bounded Variation and Free Discontinuity Problems book
Detailed Product Information
Features
| Release date (DD/MM/YYYY) | 23/03/2000 |
|---|---|
| Written by | Luigi Ambrosio, Nicola Fusco, Diego Pallara |
| Publisher | Oxford University Press |
| Suggested gender | Any gender |
| International Standard Book Number (ISBN) | 9780198502456 |
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