Fast Legendre-Fenchel transform and applications to Hamilton-Jacobi equations and conservation laws

We are interested in the study of a fast algorithm introduced by Brenier computing the discrete Legendre-Fenchel transform of a real function. We present convergence results and show how the order of convergence grows with the regularity of the Function to be transformed. applications to Hamilton-Jacobi equations for front propagation problems and conservation laws are presented.