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October  2007, 17(4): 807-819. doi: 10.3934/dcds.2007.17.807

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, Italy
2. 

Dip. di Matematica Pura e Applicata, Univ. di Padova, via Trieste 63, 35131 Padova, Italy

Received  June 2006 Revised  October 2006 Published  January 2007

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.
Keywords: PDE Aubry-Mather theory., Singular perturbations, viscosity solutions.
Mathematics Subject Classification: Primary: 35B25 ; Secondary: 49L25, 35F30, 37J5.
Citation: Fabio Camilli, Annalisa Cesaroni. A note on singular perturbation problems via Aubry-Mather theory. Discrete and Continuous Dynamical Systems, 2007, 17 (4) : 807-819. doi: 10.3934/dcds.2007.17.807
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