Generalized characteristics and Lax-Oleinik operators: global theory

Piermarco Cannarsa Universit\`a di Roma ``Tor Vergata'', Italy Wei Cheng Nanjing University, China

Analysis of PDEs mathscidoc:1701.03036

2016
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.
WeaK KAM theory; Propagation of singularity; Lax-Oleinik semi-group
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@inproceedings{piermarco2016generalized,
  title={Generalized characteristics and Lax-Oleinik operators: global theory},
  author={Piermarco Cannarsa, and Wei Cheng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170124224401558056120},
  year={2016},
}
Piermarco Cannarsa, and Wei Cheng. Generalized characteristics and Lax-Oleinik operators: global theory. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170124224401558056120.
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