Weak Kam Theory on the Wasserstein Torus with Multi-dimensional Underlying Space

@inproceedings{Tudorascu2012WeakKT,
  title={Weak Kam Theory on the Wasserstein Torus with Multi-dimensional Underlying Space},
  author={Adrian Tudorascu},
  year={2012}
}
The study of asymptotic behavior of minimizing trajectories on the Wasserstein space P(T) has so far been limited to the case d = 1 as all prior studies heavily relied on the isometric identification of P(T) with a subset of the Hilbert space L(0, 1). There is no known analogue isometric identification when d > 1. In this article we propose a new approach, intrinsic to the Wasserstein space, which allows us to prove a weak KAM theorem on P(T), the space of probability measures on the torus, for… CONTINUE READING