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.

Cannarsa, P., Cheng, W., Fathi, A. (2017). On the topology of the set of singularities of a solution to the Hamilton–Jacobi equation|Sur la topologie des singularités d'une solution de l'équation de Hamilton–Jacobi. COMPTES RENDUS MATHÉMATIQUE, 355(2), 176-180 [10.1016/j.crma.2016.12.004].

On the topology of the set of singularities of a solution to the Hamilton–Jacobi equation|Sur la topologie des singularités d'une solution de l'équation de Hamilton–Jacobi

CANNARSA, PIERMARCO;
2017-01-01

Abstract

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.
2017
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Hamilton-Jacobi equations; weak KAM theory; singularities; homotopy equivalence
Work supported by the University of Rome Tor Vergata: Consolidate the Foundation 2014 Project “Irreversibility in Dynamic Optimization” and Istituto Nazionale di Alta Matematica: GNAMPA 2016 Project “Controllo, regolarità e viabilità per alcuni tipi di equazioni diffusive” (INdAM).
http://dx.doi.org/10.1016/j.crma.2016.12.004
Cannarsa, P., Cheng, W., Fathi, A. (2017). On the topology of the set of singularities of a solution to the Hamilton–Jacobi equation|Sur la topologie des singularités d'une solution de l'équation de Hamilton–Jacobi. COMPTES RENDUS MATHÉMATIQUE, 355(2), 176-180 [10.1016/j.crma.2016.12.004].
Cannarsa, P; Cheng, W; Fathi, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/181782
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