TY  - BOOK
AU  - 
ED  - SpringerLink (Online service)
TI  - Surface Evolution Equations: A Level Set Approach 
T2  - Monographs in Mathematics
SN  - 9783764373917
AV  - QA370-380 
U1  - 515.353 23
PY  - 2006///
CY  - Basel
PB  - Birkhuser Basel
KW  - Mathematics
KW  - Differential equations, partial
KW  - Global differential geometry
KW  - Mathematical physics
KW  - Partial Differential Equations
KW  - Differential Geometry
KW  - Mathematical Methods in Physics
N1  - Surface evolution equations -- Viscosity solutions -- Comparison principle -- Classical level set method -- Set-theoretic approach
N2  - 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
UR  - http://dx.doi.org/10.1007/3-7643-7391-1
ER  -