An infinite-dimensional Weak KAM theory via random variables
Dynamical Systems
2015-08-04 v1 Analysis of PDEs
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.
Cite
@article{arxiv.1508.00154,
title = {An infinite-dimensional Weak KAM theory via random variables},
author = {Diogo Gomes and Levon Nurbekyan},
journal= {arXiv preprint arXiv:1508.00154},
year = {2015}
}