Lecture notes on geometric evolution problems, distance function and viscosity solutions
Luigi Ambrosio · OpenGrey (Institut de l'Information Scientifique et Technique) · 1997
These notes are aimed to a self contained presentation of the applications of viscosity theory to geometric evolution problems. In particular, the notes are concerned with flow by mean curvature problems for surfaces of any dimension and codimension. In codimension one, several approches to this problem are compared: the level set approach, the barrier approach, the distance approach, the approximation by solutions of the reaction diffusion equation. A crucial role in the analysis of these connections is played by the distance function, the signed distance function and the squared distance functions, whose properties are analyzed with particular attention. EMAIL:: [email protected]