Overview
- Presents results in a synthetic way with full proofs
- The audience is introduced to details of the theory as well as to its flavour
- No familiarity with differential geometry or the theory of viscosity solutions is required. Only prerequisites are calculus, linear algebra and some knowledge about semicontinuous functions
- Includes supplementary material: sn.pub/extras
Part of the book series: Monographs in Mathematics (MMA, volume 99)
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Table of contents (6 chapters)
Keywords
About this book
This book presents a self-contained introduction to the analytic foundation of a level set approach for various surface evolution equations including curvature flow equations. These equations are important in many applications, such as material sciences, image processing and differential geometry. The goal is to introduce a generalized notion of solutions allowing singularities, and to solve the initial-value problem globally-in-time in a generalized sense. Various equivalent definitions of solutions are studied. Several new results on equivalence are also presented. Moreover, structures of level set equations are studied in detail. Further, a rather complete introduction to the theory of viscosity solutions is contained, which is a key tool for the level set approach.
Although most of the results in this book are more or less known, they are scattered in several references, sometimes without proofs. This book presents these results in a synthetic way with full proofs.
The intended audience are graduate students and researchers in various disciplines who would like to know the applicability and detail of the theory as well as its flavour. No familiarity with differential geometry or the theory of viscosity solutions is required. Only prerequisites are calculus, linear algebra and some basic knowledge about semicontinuous functions.
Reviews
In view of its detailed and thorough presentation this book will be a valuable source for everyone interested in the level set approach to surface evolution equations.
Zentralblatt MATH
Authors and Affiliations
Bibliographic Information
Book Title: Surface Evolution Equations
Book Subtitle: A Level Set Approach
Authors: Yoshikazu Giga
Series Title: Monographs in Mathematics
DOI: https://doi.org/10.1007/3-7643-7391-1
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2006
Hardcover ISBN: 978-3-7643-2430-8Published: 19 January 2006
eBook ISBN: 978-3-7643-7391-7Published: 30 March 2006
Series ISSN: 1017-0480
Series E-ISSN: 2296-4886
Edition Number: 1
Number of Pages: XII, 264
Topics: Partial Differential Equations, Differential Geometry, Mathematical Methods in Physics