Generalized characteristics and Lax-Oleinik operators: global theory
Dynamical Systems
2016-05-25 v1 Analysis of PDEs
Optimization and Control
Abstract
For autonomous Tonelli systems on , we develop an intrinsic proof of the existence of generalized characteristics using sup-convolutions. This approach, together with convexity estimates for the fundamental solution, leads to new results such as the global propagation of singularities along generalized characteristics.
Keywords
Cite
@article{arxiv.1605.07581,
title = {Generalized characteristics and Lax-Oleinik operators: global theory},
author = {Piermarco Cannarsa and Wei Cheng},
journal= {arXiv preprint arXiv:1605.07581},
year = {2016}
}