EIKONAL EQUATIONS ON METRIC SPACES (Women in Mathematics)

Abstract

Given an equation |∇u|= 1, how do we solve it? What kind of functions should we call it the solutions to this so-called eikonal equation? In this talk, we will focus on this simple equation, a special case of the Hamilton-Jacobi equation. The Hamilton-Jacobi equation in general metric spaces recently attracts a great deal of attention because of its broad applications in optimal transport, traffic flow, networks, etc. We will first give a review of basic results of eikonal equation in the Euclidean space and introduce some recent development of this equation on metric spaces.