Weak KAM Theory topics in the stationary ergodic setting

Abstract : We perform a qualitative analysis of the critical equation associated with a stationary ergodic Hamiltonian through a stochastic version of the metric method, where the notion of closed random stationary set, issued from stochastic geometry, plays a major role. Our purpose is to give an appropriate notion of random Aubry set, to single out characterizing conditions for the existence of exact or approximate correctors, and write down representation formulae for them. For the last task, we make use of a Lax--type formula, adapted to the stochastic environment. This material can be regarded as a first step of a long--term project to develop a random analog of Weak KAM Theory, generalizing what done in the periodic case or, more generally, when the underlying space is a compact manifold.
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Calculus of Variations and Partial Differential Equations, Springer Verlag, 2011, 〈10.1007/s00526-011-0436-5〉
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Soumis le : lundi 16 janvier 2012 - 16:14:40
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

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Andrea Davini, Antonio Siconolfi. Weak KAM Theory topics in the stationary ergodic setting. Calculus of Variations and Partial Differential Equations, Springer Verlag, 2011, 〈10.1007/s00526-011-0436-5〉. 〈hal-00660431〉

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