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A note on singular perturbation problems via Aubry-Mather theory

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  • Exploiting the metric approach to Hamilton-Jacobi equation recently introduced by Fathi and Siconolfi [13], we prove a singular perturbation result for a general class of Hamilton-Jacobi equations. Considered in the framework of small random perturbations of dynamical systems, it extends a result due to Kamin [19] to the case of a dynamical system having several attracting points inside the domain.
    Mathematics Subject Classification: Primary: 35B25 ; Secondary: 49L25, 35F30, 37J50.


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