000 03205nam a22005415i 4500
001 978-3-7643-7302-3
003 DE-He213
005 20180115171750.0
007 cr nn 008mamaa
008 100301s2005 sz | s |||| 0|eng d
020 _a9783764373023
_9978-3-7643-7302-3
024 7 _a10.1007/b137039
_2doi
050 4 _aQA315-316
050 4 _aQA402.3
050 4 _aQA402.5-QA402.6
072 7 _aPBKQ
_2bicssc
072 7 _aPBU
_2bicssc
072 7 _aMAT005000
_2bisacsh
072 7 _aMAT029020
_2bisacsh
082 0 4 _a515.64
_223
100 1 _aDavid, Guy.
_eauthor.
245 1 0 _aSingular Sets of Minimizers for the Mumford-Shah Functional
_h[electronic resource] /
_cby Guy David.
246 3 _aFerran Sunyer i Balaguer Award winning monograph
264 1 _aBasel :
_bBirkhäuser Basel,
_c2005.
300 _aXIV, 581 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematics ;
_v233
505 0 _aPresentation of the Mumford-Shah Functional -- Functions in the Sobolev Spaces W1,p -- Regularity Properties for Quasiminimizers -- Limits of Almost-Minimizers -- Pieces of C1 Curves for Almost-Minimizers -- Global Mumford-Shah Minimizers in the Plane -- Applications to Almost-Minimizers (n = 2) -- Quasi- and Almost-Minimizers in Higher Dimensions -- Boundary Regularity.
520 _aAward-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 Some time is spent on the C^1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques.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.
650 0 _aMathematics.
650 0 _aFunctional analysis.
650 0 _aPartial differential equations.
650 0 _aCalculus of variations.
650 1 4 _aMathematics.
650 2 4 _aCalculus of Variations and Optimal Control; Optimization.
650 2 4 _aFunctional Analysis.
650 2 4 _aPartial Differential Equations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783764371821
830 0 _aProgress in Mathematics ;
_v233
856 4 0 _uhttp://dx.doi.org/10.1007/b137039
912 _aZDB-2-SMA
999 _c372845
_d372845