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| by: Yoshikazu Giga |
Surface Evolution Equations: A Level Set Approach (Monographs in Mathematics)
by: Yoshikazu Giga
DOI: 1007/3-7643-7391-1 ISBN: 3764324309 9783764324308 All ISBNs: 3764324309 AFP — 9783764324308
3764373911 eBk LCCN: 2005058912 Dewey: 515/.353 22 LC Class: QA377 .G485 2006 keywords: Evolution equations;
Level set method;
Viscosity theory; Series: Mathematics, Monographs in Vol: 99 Size: 5.8 MB Topics: Evolution equations
Hamilton-Jacobi equations
Curves, Algebraic
Differential equations, Parabolic
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.
Written for:
Graduates, postgraduates and researchers; physicists, people working in image processing
Keywords:
Evolution equations
Level set method
Viscosity theory
Science
Mathematics
Analysis
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