Monographs in Mathematics

Surface Evolution Equations

A Level Set Approach

Authors: Giga, Yoshikazu

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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


Table of contents (1 chapters)

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-3-7643-7391-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-3-7643-2430-8
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
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Bibliographic Information

Bibliographic Information
Book Title
Surface Evolution Equations
Book Subtitle
A Level Set Approach
Authors
Series Title
Monographs in Mathematics
Series Volume
99
Copyright
2006
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-7391-7
DOI
10.1007/3-7643-7391-1
Hardcover ISBN
978-3-7643-2430-8
Series ISSN
1017-0480
Edition Number
1
Number of Pages
XII, 264
Topics