A note  on singular perturbation problems via Aubry-Mather theory

Fabio Camilli; Annalisa Cesaroni

doi:10.3934/dcds.2007.17.807

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2007, Volume 17, Issue 4: 807-819. Doi: 10.3934/dcds.2007.17.807

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A note on singular perturbation problems via Aubry-Mather theory

Fabio Camilli^1, and
Annalisa Cesaroni^2,

1.
Dip. di Matematica Pura e Applicata, Univ. dell’Aquila, loc. Monteluco di Roio, 67040 l’Aquila
2.
Dip. di Matematica Pura e Applicata, Univ. di Padova, via Trieste 63, 35131 Padova

Received: May 31, 2006

Revised: September 30, 2006

Published: September 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B25 ; Secondary: 49L25, 35F30, 37J50.

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