Generalized characteristics and Lax-Oleinik operators: global theory

Piermarco Cannarsa, Wei Cheng

Published 2016-05-24Version 1

For autonomous Tonelli systems on $\R^n$, 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.