Giga / Liu Surface Evolution Equations

A Level Set Approach
2. Auflage 2026
ISBN: 978-3-032-20303-8
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 392 Seiten

Reihe: Mathematics and Statistics

This monograph 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. 

For the , new chapters have been added that describe a recent approach to surface evolution equations based on deterministic discrete two-person games. This game-theoretic interpretation is used to discuss the fattening phenomenon for the curvature flow equation and to provide an alternative proof for convexity preserving properties.

This text is suitable for applied researchers who would like to know the detail of the theory, as well as its flavor; it is also suitable for graduate students interested in the field. Prerequisites include calculus, linear algebra, and some familiarity with semicontinuous functions. Familiarity with differential geometry and the theory of viscosity solutions is not required.  

Zielgruppe

Research

Autoren/Hrsg.

Giga, Yoshikazu

Liu, Qing

Inhaltsverzeichnis

Preface.- Introduction.- Surface Evolution Equations.- Viscosity Solutions.- Comparison Principle.- Classical Level Set Method.- Set-Theoretic Approach.- Deterministic Game Interpretations.- Applications of Game-Theoretic Approach.