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Surface Evolution Equations

A Level Set Approach

  • Yoshikazu Giga

Part of the Monographs in Mathematics book series (MMA, volume 99)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Pages 1-13
  3. Pages 69-107
  4. Pages 109-161
  5. Pages 207-242
  6. Back Matter
    Pages 243-264

About this book

Introduction

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.

Keywords

Evolution equations Level set method Viscosity theory curvature differential geometry

Authors and affiliations

  • Yoshikazu Giga
    • 1
  1. 1.Graduate School of Mathematical SciencesUniversity of TokyoTokyoJapan

Bibliographic information