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Surface Evolution Equations

Surface Evolution Equations
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ISBN: 9783764324308
Autor: Yoshikazu Gigi
Einband/Bindung: Buch
Sprache: Englisch
Seitenzahl: 264
Erscheinungsjahr: 2006
Verlag: Springer Basel AG
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Beschreibung
This book is intended to be a self-contained introduction to analytic foundations of a level set method for various surface evolution equations including curvature ow equations. These equations are important in various elds including material sciences, image processing and di erential geometry. The goal of this book is to introduce a generalized notion of solutions allowing singularities and solve the initial-value problem globally-in-time in a generalized sense. Various equivalent de nitions of solutions are studied. Several new results on equivalence are also presented. Wepresentherearathercompleteintroductiontothetheoryofviscosityso- tionswhichis a keytoolforthe levelsetmethod. Alsoa self-containedexplanation isgivenforgeneralsurfaceevolutionequationsofthe secondorder.Althoughmost ofthe resultsin this book aremoreor lessknown,they arescatteredinseveralr- erences, sometimes without proof. This book presents these results in a synthetic way with full proofs. However, the references are not exhaustive at all. The book is suitable for applied researchers who would like to know the detail of the theory as well as its avour.No familiarity with di erential geometry and the theory of viscosity solutions is required. The prerequisites are calculus, linear algebra and some familiarity with semicontinuous functions. This book is also suitable for upper level under graduate students who are interested in the eld.
Artikel-Nr.: 9783764324308
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