ENGLISH

Functions of Bounded Variation and Free Discontinuity Problems

By Luigi Ambrosio , Nicola Fusco , Diego Pallara

Book information

Publisher
Oxford University Press, USA
Year
2000
ISBN
0198502451, 9780198502456
LCC
QA316 .A52 2000
Open Library ID
OL22091094M
Language
english
Format
DJVU
Filesize
19 MB (20092077 bytes)
Series
Oxford Mathematical Monographs
Pages
454\454
Time added
2011-01-06 10:13:16

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 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.

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