The Lax-Oleinik semi-group on graphs
Analysis of PDEs
2017-04-28 v2
Abstract
We consider Tonelli Lagrangians on a graph, define weak KAM solutions, which happen to be the fixed points of the Lax-Oleinik semi-group, and identify their uniqueness set as the Aubry set, giving a representation formula. Our main result is the long time convergence of the Lax Oleinik semi-group. Weak KAM solutions are viscosity solutions, and in the case of Hamiltonians called of eikonal type in [CS], we prove that the converse holds.
Cite
@article{arxiv.1601.03577,
title = {The Lax-Oleinik semi-group on graphs},
author = {Renato Iturriaga and Hector Sanchez Morgado},
journal= {arXiv preprint arXiv:1601.03577},
year = {2017}
}
Comments
23 pages