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My first novel, Love Me Back, was published on September 16. Writing the book took seven years, and along the way three chapters were published in... Continue »
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Functions of Bounded Variation and Free Discontinuity Problems (Oxford Mathematical Monographs)

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

 

Synopses & Reviews

Publisher Comments:

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.

Table of Contents

Basic terminology and notation

1. Measure theory

2. Basic geometric measure theory

3. Functions of bounded variation

4. Special functions of bounded variation

5. Semicontinuity in BV

6. The Mumford-Shah functional

7. Minimisers of free continuity problems

8. Regularity of the free discontinuity set

References

Index

Product Details

ISBN:
9780198502456
Author:
Ambrosio, Luigi
Publisher:
OUP Oxford
Author:
null, Nicola
Author:
Pallara, Diego
Author:
null, Luigi
Author:
Fusco, Nicola
Author:
null, Diego
Location:
Oxford
Subject:
Calculus
Subject:
Applied
Subject:
Functional Analysis
Subject:
Calculus of variations
Subject:
Functions of bounded variation.
Subject:
Mathematics | Applied Mathematics
Subject:
Mathematics-Calculus
Edition Description:
Includes bibliographical references and index.
Series:
Oxford mathematical monographs
Series Volume:
episode 10
Publication Date:
20000331
Binding:
HARDCOVER
Grade Level:
College/higher education:
Language:
English
Illustrations:
23 halftones and line illus
Pages:
456
Dimensions:
6.1 x 9.3 x 1.2 in 2.431 lb

Related Subjects


Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Functional Analysis

Functions of Bounded Variation and Free Discontinuity Problems (Oxford Mathematical Monographs) New Hardcover
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Product details 456 pages Oxford University Press - English 9780198502456 Reviews:
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