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.
Original language | English (US) |
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Pages (from-to) | 6167-6185 |
Number of pages | 19 |
Journal | Discrete and Continuous Dynamical Systems |
Volume | 36 |
Issue number | 11 |
DOIs | |
State | Published - Aug 31 2016 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledgements: 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.