| 书目名称 | Singular Sets of Minimizers for the Mumford-Shah Functional |
| 编辑 | Guy David |
| 视频video | |
| 概述 | Contains the first systematic account of Bonnet‘s blow-up and monotonicity methods.Fairly accessible, self-contained, and detailed.Many new results and unpublished proofs |
| 丛书名称 | Progress in Mathematics |
| 图书封面 |  |
| 描述 | .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 Some time is spent on the C^1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet‘s monotonicity and blow-up techniques.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.. |
| 出版日期 | Book 2005 |
| 关键词 | Minimierungsprobleme; Mumford-Shah-Funktional; Randwertprobleme; Sobolev space; Variationsrechnung; parti |
| 版次 | 1 |
| doi | https://doi.org/10.1007/b137039 |
| isbn_ebook | 978-3-7643-7302-3Series ISSN 0743-1643 Series E-ISSN 2296-505X |
| issn_series | 0743-1643 |
| copyright | Birkhäuser Basel 2005 |
发表于 2025-3-21 18:03:39
