An infinite-dimensional weak KAM theory via random variables

Abstract
We develop several aspects of the infinite-dimensional Weak KAM theory using a random variables' approach. We prove that the infinite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on R.

Citation
Gomes D, Nurbekyan L (2016) An infinite-dimensional weak KAM theory via random variables. Discrete and Continuous Dynamical Systems 36: 6167–6185. Available: http://dx.doi.org/10.3934/dcds.2016069.

Acknowledgements
The first author was partially supported by KAUST baseline and start-up funds and KAUST SRI, Center for Uncertainty Quanti cation in Computational Science and Engineering.

Publisher
American Institute of Mathematical Sciences (AIMS)

Journal
Discrete and Continuous Dynamical Systems

DOI
10.3934/dcds.2016069

arXiv
1508.00154

Additional Links
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=12901http://arxiv.org/pdf/1508.00154

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