Generalized characteristics and Lax-Oleinik operators: global theory

Abstract

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

References in corpus (2)

• Weak KAM theorem on non compact manifolds
• Homoclinic orbits and critical points of barrier functions

Cited by in corpus (1)

• Lasry-Lions, Lax-Oleinik and Generalized characteristics