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Functions of Bounded Variation and Free Discontinuity Problems (Oxford Mathematical Monographs) Hardcover – 23 Mar 2000


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Product details

  • Hardcover: 456 pages
  • Publisher: OUP Oxford (23 Mar. 2000)
  • Language: English
  • ISBN-10: 0198502451
  • ISBN-13: 978-0198502456
  • Product Dimensions: 23.6 x 3 x 15.5 cm
  • Average Customer Review: Be the first to review this item
  • Amazon Bestsellers Rank: 4,386,755 in Books (See Top 100 in Books)
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Product description

Review

... an excellent account of the theory of BV functions. It should serve as a standard reference, especially for the BV theory, for years to come. (Bulletin of the London Mathematical Society)

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 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.


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Amazon.com: 5.0 out of 5 stars 2 reviews
M. Wyatt
5.0 out of 5 starsExcellent book for research purposes
19 March 2014 - Published on Amazon.com
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5.0 out of 5 starsSurvey on BV theory in Euclidean setting
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