Front tracking and iterated minmax for Hamilton-Jacobi equation in one space variable

Abstract

The viscosity solution of the Hamilton-Jacobi equation was constructed by an "iterated minimax" procedure. Using Dafermos' front tracking method, we give another proof of this construction in the case of Hamilton-Jacobi equations in one space dimension. This allows us to get a better understanding in this case of the singularities of the viscosity solution.