Functions of bounded variation and free discontinuity problems
Author(s)
Bibliographic Information
Functions of bounded variation and free discontinuity problems
(Oxford mathematical monographs)
Clarendon Press, 2000
- : hbk
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hbkAMB||7||101022773
Note
Includes bibliographical references (p. [419]-430) and index
Description and Table of Contents
Description
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.
Table of Contents
- Measure Theory
- Basic Geometric Measure Theory
- Functions of bounded variation
- Special functions of bounded variation
- Semicontinuity in BV
- The Mumford-Shah functional
- Minimisers of free continuity problems
- Regularity of the free discontinuity set
- References
- Index
by "Nielsen BookData"