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Progress in Mathematics
cover

Singular Sets of Minimizers for the Mumford-Shah Functional

Authors: David, Guy

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  • ISBN 978-3-7643-7302-3
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Hardcover $169.99
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  • ISBN 978-3-7643-7182-1
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About this book

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2004.

This book studies regularity properties of Mumford-Shah minimizers. The Mumford-Shah functional was introduced in the 1980s as a tool for automatic image segmentation, but its study gave rise to many interesting questions of analysis and geometric measure theory. The main object under scrutiny is a free boundary K where the minimizer may have jumps. The book presents an extensive description of the known regularity properties of the singular sets K, and the techniques to get them. Some time is spent on the C^1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques. In particular, global minimizers in the plane are studied in full detail.
The book is largely self-contained and should be accessible to graduate students in analysis.The core of the book is composed of regularity results that were proved in the last ten years and which are presented in a more detailed and unified way.

Reviews

From the reviews:

“This monograph is the Ferran Sunyer i Balaguer 2004 prize winner.The book under review gives an excellent overview of a part of the work done in recent years on this problem … and the book is therefore a useful source for mathematicians working in this field.”(MATHEMATICAL REVIEWS)


Table of contents (9 chapters)

Table of contents (9 chapters)
  • Presentation of the Mumford-Shah Functional

    Pages 1-61

  • Functions in the Sobolev Spaces W1,p

    Pages 63-104

  • Regularity Properties for Quasiminimizers

    Pages 105-205

  • Limits of Almost-Minimizers

    Pages 207-269

  • Pieces of C1 Curves for Almost-Minimizers

    Pages 271-354

Buy this book

eBook $129.00
price for USA in USD
  • ISBN 978-3-7643-7302-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-3-7643-7182-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Singular Sets of Minimizers for the Mumford-Shah Functional
Authors
Series Title
Progress in Mathematics
Series Volume
233
Copyright
2005
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-7302-3
DOI
10.1007/b137039
Hardcover ISBN
978-3-7643-7182-1
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XIV, 581
Topics