On the convergence of singular perturbations of Hamilton-Jacobi equations

Claudio Marchi

doi:10.3934/cpaa.2010.9.1363

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2010, Volume 9, Issue 5: 1363-1377. Doi: 10.3934/cpaa.2010.9.1363

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On the convergence of singular perturbations of Hamilton-Jacobi equations

Claudio Marchi^1,

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

Received: August 31, 2009

Revised: November 30, 2009

Published: August 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B25; Secondary: 49L25, 35B27.

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