03070nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020001800100024002500118050001400143050001200157050002000169072001700189072001600206072002300222072002300245082001500268100002500283245010400308246005300412264004000465300003400505336002600539337002600565338003600591347002400627490003500651505037800686520109101064650001702155650002502172650003602197650002802233650001702261650006202278650002502340650003602365710003402401773002002435776003602455830003502491856003802526978-3-7643-7302-3DE-He21320180115171750.0cr nn 008mamaa100301s2005 sz | s |||| 0|eng d a97837643730237 a10.1007/b1370392doi 4aQA315-316 4aQA402.3 4aQA402.5-QA402.6 7aPBKQ2bicssc 7aPBU2bicssc 7aMAT0050002bisacsh 7aMAT0290202bisacsh04a515.642231 aDavid, Guy.eauthor.10aSingular Sets of Minimizers for the Mumford-Shah Functionalh[electronic resource] /cby Guy David.3 aFerran Sunyer i Balaguer Award winning monograph 1aBasel :bBirkhàˆuser Basel,c2005. aXIV, 581 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aProgress in Mathematics ;v2330 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. 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 Some time is spent on the C^1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques.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. 0aMathematics. 0aFunctional analysis. 0aPartial differential equations. 0aCalculus of variations.14aMathematics.24aCalculus of Variations and Optimal Control; Optimization.24aFunctional Analysis.24aPartial Differential Equations.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9783764371821 0aProgress in Mathematics ;v23340uhttp://dx.doi.org/10.1007/b137039