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September  2010, 9(5): 1363-1377. doi: 10.3934/cpaa.2010.9.1363

## On the convergence of singular perturbations of Hamilton-Jacobi equations

 1 Dipartimento di Matematica Pura ed Applicata, Università di Padova, via Trieste 63, 35121 Padova, Italy

Received  September 2009 Revised  December 2009 Published  May 2010

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.
Citation: Claudio Marchi. On the convergence of singular perturbations of Hamilton-Jacobi equations. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1363-1377. doi: 10.3934/cpaa.2010.9.1363
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