On the topology of the set of singularities of a solution of the Hamilton-Jacobi equation

Piermarco Cannarsa Universit\`a di Roma ``Tor Vergata'', Italy Wei Cheng Nanjing University, China Albert Fathi ENS de Lyon \& IUF, France

Analysis of PDEs mathscidoc:1701.03035

Distinguished Paper Award in 2017

2016
We address the topology of the set of singularities of a solution of a Hamilton-Jacobi equation. For this we will apply the idea of the first two authors (Generalized characteristic and Lax-Oleinik operators: global result, preprint, arXiv:1605.07581, 2016.) to use the positive Lax-Oleinik semi-group to propagate singularities. {\it To cite this article: P. Cannarsa, W. Cheng, A. Fathi, C. R. Acad. Sci. Paris, Ser. I 340 (2005).
weak KAM theory; Singularity; Cut Locus; Local contractible
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@inproceedings{piermarco2016on,
  title={On the topology of the set of singularities of a solution of the Hamilton-Jacobi equation},
  author={Piermarco Cannarsa, Wei Cheng, and Albert Fathi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170124223310554087119},
  year={2016},
}
Piermarco Cannarsa, Wei Cheng, and Albert Fathi. On the topology of the set of singularities of a solution of the Hamilton-Jacobi equation. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170124223310554087119.
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