On the convergence of singular perturbations of Hamilton-Jacobi equations

This paper is devoted to singular perturbation problems for first order equations. Under some coercivity and periodicity assumptions, we establish the uniform convergence and we provide an estimate of the rate of convergence, which we consider the main result of the paper. We shall also show that our results apply to the homogenization problem for coercive and periodic equations. Finally, some examples arising in optimal control and differential games theory will be discussed.