[Sur la topologie des singularités d'une solution de l'équation de Hamilton–Jacobi]
Nous étudions l'ensemble des singularités d'une solution de l'équation de Hamilton–Jacobi. Pour cette étude, nous utilisons une idée due aux deux premiers auteurs (Cannarsa and Cheng, Generalized characteristics and Lax–Oleinik operators: global result, preprint, arXiv:1605.07581, 2016) pour propager les singularités en utilisant le semi-groupe positif de Lax–Oleinik.
We address the topology of the set of singularities of a solution to a Hamilton–Jacobi equation. For this, we will apply the idea of the first two authors (Cannarsa and Cheng, Generalized characteristics and Lax–Oleinik operators: global result, preprint, arXiv:1605.07581, 2016) to use the positive Lax–Oleinik semi-group to propagate singularities.
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@article{CRMATH_2017__355_2_176_0,
author = {Cannarsa, Piermarco and Cheng, Wei and Fathi, Albert},
title = {On the topology of the set of singularities of a solution to the {Hamilton{\textendash}Jacobi} equation},
journal = {Comptes Rendus. Math\'ematique},
pages = {176--180},
publisher = {Elsevier},
volume = {355},
number = {2},
year = {2017},
doi = {10.1016/j.crma.2016.12.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.12.004/}
}
TY - JOUR AU - Cannarsa, Piermarco AU - Cheng, Wei AU - Fathi, Albert TI - On the topology of the set of singularities of a solution to the Hamilton–Jacobi equation JO - Comptes Rendus. Mathématique PY - 2017 SP - 176 EP - 180 VL - 355 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.12.004/ DO - 10.1016/j.crma.2016.12.004 LA - en ID - CRMATH_2017__355_2_176_0 ER -
%0 Journal Article %A Cannarsa, Piermarco %A Cheng, Wei %A Fathi, Albert %T On the topology of the set of singularities of a solution to the Hamilton–Jacobi equation %J Comptes Rendus. Mathématique %D 2017 %P 176-180 %V 355 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.12.004/ %R 10.1016/j.crma.2016.12.004 %G en %F CRMATH_2017__355_2_176_0
Cannarsa, Piermarco; Cheng, Wei; Fathi, Albert. On the topology of the set of singularities of a solution to the Hamilton–Jacobi equation. Comptes Rendus. Mathématique, Tome 355 (2017) no. 2, pp. 176-180. doi : 10.1016/j.crma.2016.12.004. http://www.numdam.org/articles/10.1016/j.crma.2016.12.004/
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