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

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